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One class of generalized boundary value problem for analytic functions | Boundary Value Problems | Full Text
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Therefore, the classic Riemann boundary value problem is extended further."/> <meta name="journal_id" content="13661"/> <meta name="dc.title" content="One class of generalized boundary value problem for analytic functions"/> <meta name="dc.source" content="Boundary Value Problems 2015 2015:1"/> <meta name="dc.format" content="text/html"/> <meta name="dc.publisher" content="SpringerOpen"/> <meta name="dc.date" content="2015-02-24"/> <meta name="dc.type" content="OriginalPaper"/> <meta name="dc.language" content="En"/> <meta name="dc.copyright" content="2015 Li; licensee Springer."/> <meta name="dc.rights" content="2015 Li; licensee Springer."/> <meta name="dc.rightsAgent" content="reprints@biomedcentral.com"/> <meta name="dc.description" content="In this paper, a boundary value problem for analytic functions with two unknown functions on two parallel straight lines is studied, the general solutions in the different domains as well as the conditions of solvability are obtained in class $\{1\}$ , and the behaviors of solutions are discussed at $z=\infty$ and in the different domains, respectively. Therefore, the classic Riemann boundary value problem is extended further."/> <meta name="prism.issn" content="1687-2770"/> <meta name="prism.publicationName" content="Boundary Value Problems"/> <meta name="prism.publicationDate" content="2015-02-24"/> <meta name="prism.volume" content="2015"/> <meta name="prism.number" content="1"/> <meta name="prism.section" content="OriginalPaper"/> <meta name="prism.startingPage" content="1"/> <meta name="prism.endingPage" content="11"/> <meta name="prism.copyright" content="2015 Li; licensee Springer."/> <meta name="prism.rightsAgent" content="reprints@biomedcentral.com"/> <meta name="prism.url" content="https://boundaryvalueproblems.springeropen.com/articles/10.1186/s13661-015-0301-0"/> <meta name="prism.doi" content="doi:10.1186/s13661-015-0301-0"/> <meta name="citation_pdf_url" content="https://boundaryvalueproblems.springeropen.com/counter/pdf/10.1186/s13661-015-0301-0"/> <meta name="citation_fulltext_html_url" content="https://boundaryvalueproblems.springeropen.com/articles/10.1186/s13661-015-0301-0"/> <meta name="citation_journal_title" content="Boundary Value Problems"/> <meta name="citation_journal_abbrev" content="Bound Value Probl"/> <meta name="citation_publisher" content="SpringerOpen"/> <meta name="citation_issn" content="1687-2770"/> <meta name="citation_title" content="One class of generalized boundary value problem for analytic functions"/> <meta name="citation_volume" content="2015"/> <meta name="citation_issue" content="1"/> <meta name="citation_publication_date" content="2015/12"/> <meta name="citation_online_date" content="2015/02/24"/> <meta name="citation_firstpage" content="1"/> <meta name="citation_lastpage" content="11"/> <meta name="citation_article_type" content="Research"/> <meta name="citation_fulltext_world_readable" content=""/> <meta name="citation_language" content="en"/> <meta name="dc.identifier" content="doi:10.1186/s13661-015-0301-0"/> <meta name="DOI" content="10.1186/s13661-015-0301-0"/> <meta name="size" content="666364"/> <meta name="citation_doi" content="10.1186/s13661-015-0301-0"/> <meta name="citation_springer_api_url" content="http://api.springer.com/xmldata/jats?q=doi:10.1186/s13661-015-0301-0&api_key="/> <meta name="description" content="In this paper, a boundary value problem for analytic functions with two unknown functions on two parallel straight lines is studied, the general solutions in the different domains as well as the conditions of solvability are obtained in class $\{1\}$ , and the behaviors of solutions are discussed at $z=\infty$ and in the different domains, respectively. 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Therefore, the classic Riemann boundary value problem is extended further."/> <meta property="og:image" content="https://media.springernature.com/full/springer-static/cover-hires/journal/13661"/> <script type="application/ld+json">{"mainEntity":{"headline":"One class of generalized boundary value problem for analytic functions","description":"In this paper, a boundary value problem for analytic functions with two unknown functions on two parallel straight lines is studied, the general solutions in the different domains as well as the conditions of solvability are obtained in class \n \n \n \n \n \n \n $\\{1\\}$\n , and the behaviors of solutions are discussed at \n \n \n \n \n \n \n $z=\\infty$\n and in the different domains, respectively. 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generalized boundary value problem for analytic functions </div> <div class="c-pdf-container"> <div class="c-pdf-download u-clear-both"> <a href="//boundaryvalueproblems.springeropen.com/counter/pdf/10.1186/s13661-015-0301-0.pdf" class="u-button u-button--full-width u-button--primary u-justify-content-space-between c-pdf-download__link" data-article-pdf="true" data-readcube-pdf-url="true" data-test="pdf-link" data-draft-ignore="true" data-track="content_download" data-track-type="article pdf download" data-track-action="download pdf" data-track-label="link" data-track-external download> <span class="c-pdf-download__text">Download PDF</span> <svg aria-hidden="true" focusable="false" width="16" height="16" class="u-icon"><use xlink:href="#icon-download"/></svg> </a> </div> </div> </div> </div> <div class="c-pdf-button__container u-hide-at-lg js-context-bar-sticky-point-mobile"> <div class="c-pdf-container" data-track-context="article body"> <div class="c-pdf-download u-clear-both"> <a 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href="https://www.springernature.com/gp/open-research/about/the-fundamentals-of-open-access-and-open-research" data-track="click" data-track-action="open access" data-track-label="link" class="u-color-open-access" data-test="open-access">Open access</a> </li> <li class="c-article-identifiers__item">Published: <time datetime="2015-02-24">24 February 2015</time></li> </ul> <h1 class="c-article-title" data-test="article-title" data-article-title="">One class of generalized boundary value problem for analytic functions</h1> <ul class="c-article-author-list c-article-author-list--short" data-test="authors-list" data-component-authors-activator="authors-list"><li class="c-article-author-list__item"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-Pingrun-Li-Aff1" data-author-popup="auth-Pingrun-Li-Aff1" data-author-search="Li, Pingrun" data-corresp-id="c1">Pingrun Li<svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-mail-medium"></use></svg></a><sup class="u-js-hide"><a href="#Aff1">1</a></sup> </li></ul> <p class="c-article-info-details" data-container-section="info"> <a data-test="journal-link" href="/" data-track="click" data-track-action="journal homepage" data-track-category="article body" data-track-label="link"><i data-test="journal-title">Boundary Value Problems</i></a> <b data-test="journal-volume"><span class="u-visually-hidden">volume</span> 2015</b>, Article number: <span data-test="article-number">40</span> (<span data-test="article-publication-year">2015</span>) <a href="#citeas" class="c-article-info-details__cite-as u-hide-print" data-track="click" data-track-action="cite this article" data-track-label="link">Cite this article</a> </p> <div class="c-article-metrics-bar__wrapper u-clear-both"> <ul class="c-article-metrics-bar u-list-reset"> <li class=" c-article-metrics-bar__item" data-test="access-count"> <p class="c-article-metrics-bar__count">1376 <span class="c-article-metrics-bar__label">Accesses</span></p> </li> <li class="c-article-metrics-bar__item"> <p class="c-article-metrics-bar__details"><a href="/articles/10.1186/s13661-015-0301-0/metrics" data-track="click" data-track-action="view metrics" data-track-label="link" rel="nofollow">Metrics <span class="u-visually-hidden">details</span></a></p> </li> </ul> </div> </div> <section aria-labelledby="Abs1" data-title="Abstract" lang="en"><div class="c-article-section" id="Abs1-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Abs1">Abstract</h2><div class="c-article-section__content" id="Abs1-content"><p>In this paper, a boundary value problem for analytic functions with two unknown functions on two parallel straight lines is studied, the general solutions in the different domains as well as the conditions of solvability are obtained in class <span class="mathjax-tex">\(\{1\}\)</span>, and the behaviors of solutions are discussed at <span class="mathjax-tex">\(z=\infty\)</span> and in the different domains, respectively. Therefore, the classic Riemann boundary value problem is extended further.</p></div></div></section> <section data-title="Introduction and preliminaries"><div class="c-article-section" id="Sec1-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Sec1"><span class="c-article-section__title-number">1 </span>Introduction and preliminaries</h2><div class="c-article-section__content" id="Sec1-content"><p>Many mathematicians have studied the boundary value problems of analytic functions and formed a perfect theoretical system; see [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 1" title="
					Lu, JK: Boundary Value Problems for Analytic Functions. World Scientific, Singapore (2004)
				" href="/articles/10.1186/s13661-015-0301-0#ref-CR1" id="ref-link-section-d243226627e359">1</a>–<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 7" title="
					Lu, JK: Some classes boundary value problems and singular integral equations with a transformation. Adv. Math. 23(5), 424-431 (1994)
				" href="/articles/10.1186/s13661-015-0301-0#ref-CR7" id="ref-link-section-d243226627e362">7</a>]. The boundary value problem of analytic functions on an infinite straight line has been studied in the literature, and there has been a brief description of boundary value problems of analytic function with an unknown function on several parallel lines. In this paper, we will put forward the boundary value problems of analytic functions with two unknown functions on two parallel lines and a general method different from the one in classical boundary value theory. Moreover, we will give and discuss the general solution and solvability conditions, which will generalize the classical theory of boundary value problems of analytic functions.</p><p>Let us describe the definitions of <i>Plemelj</i> formula and function class <span class="mathjax-tex">\(\{1\}\)</span> on an infinite straight line.</p> <h3 class="c-article__sub-heading" id="FPar1">Definition 1.1</h3> <p>Assume that <span class="mathjax-tex">\(\omega(x)\)</span> is a continuous complex function on the real axis <i>X</i>. We say that <span class="mathjax-tex">\(\omega(x)\in\hat{H}\)</span> if the following conditions hold: </p><ol class="u-list-style-none"> <li> <span class="u-custom-list-number">(1)</span> <p>For any sufficiently large positive number <i>M</i>, <span class="mathjax-tex">\(\omega(x)\)</span> satisfies <span class="mathjax-tex">\(\omega(x)\in H\)</span> on <span class="mathjax-tex">\([-M,M]\)</span> (see [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 8" title="
					Li, PR: On the method of solving two kinds of convolution singular integral equations with reflection. Ann. Differ. Equ. 29(2), 159-166 (2013)
				" href="/articles/10.1186/s13661-015-0301-0#ref-CR8" id="ref-link-section-d243226627e575">8</a>] for the definition of <i>H</i>).</p> </li> <li> <span class="u-custom-list-number">(2)</span> <p> <span class="mathjax-tex">\(|\omega(x_{1})-\omega(x_{2})|\leq A|\frac{1}{x_{1}}-\frac{1}{x_{2}}|\)</span>, for any <span class="mathjax-tex">\(|x_{j}|>M\)</span> (<span class="mathjax-tex">\(j=1,2\)</span>) and some positive real number <i>A</i>.</p> </li> </ol> <p>Under condition (2), we say that <span class="mathjax-tex">\(\omega(x)\)</span> satisfies the Hölder condition on <span class="mathjax-tex">\(N_{\infty}\)</span> and denote it <span class="mathjax-tex">\(\omega(x)\in H(N_{\infty})\)</span>, where <span class="mathjax-tex">\(N_{\infty}=\{x: |x|>M\}\)</span> is a neighborhood of ∞.</p> <h3 class="c-article__sub-heading" id="FPar2">Definition 1.2</h3> <p>Assume that <span class="mathjax-tex">\(\omega(x)\)</span> is continuous on <span class="mathjax-tex">\((-\infty, \infty)\)</span> and <span class="mathjax-tex">\(\int_{-\infty}^{\infty}|\omega(x)|\, dx<+\infty\)</span>, then we say that <span class="mathjax-tex">\(\omega(x)\in L_{1}(-\infty,\infty)\)</span>.</p> <h3 class="c-article__sub-heading" id="FPar3">Definition 1.3</h3> <p>If <span class="mathjax-tex">\(\omega(x)\)</span> satisfies: (1) <span class="mathjax-tex">\(\omega(x)\in\hat {H}\)</span>, (2) <span class="mathjax-tex">\(\omega(x)\in L_{1}(-\infty,\infty)\)</span>, then we say that <span class="mathjax-tex">\(\omega (x)\)</span> belongs to the function class <span class="mathjax-tex">\(\{1\}\)</span>.</p> <h3 class="c-article__sub-heading" id="FPar4">Definition 1.4</h3> <p>Assume that <span class="mathjax-tex">\(\omega(x)\in\{1\}\)</span>, then the integrals <span class="mathjax-tex">\(\Omega^{+}(z)=\frac{1}{\sqrt{2\pi}}\int_{0}^{+\infty}\omega (t)e^{itz}\, dt\)</span> and <span class="mathjax-tex">\(\Omega^{-}(z)=\frac{1}{\sqrt{2\pi}}\int_{-\infty }^{0}\omega(t)e^{itz}\, dt\)</span> are called the left and right one-sided Fourier integral, respectively.</p> <h3 class="c-article__sub-heading" id="FPar5">Lemma 1.1</h3> <p>(see [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 1" title="
					Lu, JK: Boundary Value Problems for Analytic Functions. World Scientific, Singapore (2004)
				" href="/articles/10.1186/s13661-015-0301-0#ref-CR1" id="ref-link-section-d243226627e1521">1</a>])</p> <p> <i>If</i> <span class="mathjax-tex">\(\omega(z)\in H\)</span> <i>with respect to any finite part of some infinite domain</i> <i>D</i>, <i>and</i> <span class="mathjax-tex">\(\omega(z)\)</span> <i>is analytic in any neighborhood of infinity</i>, <i>then</i> <span class="mathjax-tex">\(\omega(z)\in\hat{H}\)</span>.</p> <h3 class="c-article__sub-heading" id="FPar6">Lemma 1.2</h3> <p>(see [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 2" title="
					Muskhelishvilli, NI: Singular Integral Equations. Nauka, Moscow (2002)
				" href="/articles/10.1186/s13661-015-0301-0#ref-CR2" id="ref-link-section-d243226627e1651">2</a>])</p> <p> <i>If</i> <span class="mathjax-tex">\(\omega(t)\)</span> <i>belongs to the class</i> <span class="mathjax-tex">\(\{1\} \)</span>, <i>then the left and right one</i>-<i>sided Fourier integrals defined in Definition </i> <a data-track="click" data-track-label="link" data-track-action="subsection anchor" href="/articles/10.1186/s13661-015-0301-0#FPar4">1.4</a> <i>are analytic when</i> <span class="mathjax-tex">\(\operatorname{Im} z>0\)</span> <i>and</i> <span class="mathjax-tex">\(\operatorname{Im} z<0\)</span>, <i>respectively</i>.</p> <h3 class="c-article__sub-heading" id="FPar7">Lemma 1.3</h3> <p>(see [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 8" title="
					Li, PR: On the method of solving two kinds of convolution singular integral equations with reflection. Ann. Differ. Equ. 29(2), 159-166 (2013)
				" href="/articles/10.1186/s13661-015-0301-0#ref-CR8" id="ref-link-section-d243226627e1793">8</a>])</p> <p> <i>If</i> <span class="mathjax-tex">\(\omega(x)\in\hat{H}\)</span>, <i>we have the Cauchy type integral</i> <span class="mathjax-tex">\(\Omega(z)=\frac{1}{2\pi i}\int_{-\infty}^{\infty }\frac{\omega(t)}{t-z}\, dt\)</span>, <span class="mathjax-tex">\(z\notin(-\infty,\infty)\)</span>, <i>then the following formula holds on the infinite straight line</i>: </p><div id="Equa" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$\Omega^{\pm}(x)=\pm\frac{1}{2}\omega(x)+\Omega(x),\quad \textit{i.e.},\quad \Omega^{\pm }(x)=\pm\frac{1}{2}\omega(x)+ \frac{1}{2\pi i}\int_{-\infty}^{\infty}\frac{\omega(t)}{t-x}\, dt. $$</span></div></div> </div></div></section><section data-title="Problem presentation"><div class="c-article-section" id="Sec2-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Sec2"><span class="c-article-section__title-number">2 </span>Problem presentation</h2><div class="c-article-section__content" id="Sec2-content"><p>Now, we put forward the boundary value problem of analytic functions on two parallel lines.</p><p>Without loss of generality, we assume that the two lines are parallel to the <i>X</i>-axis (otherwise, we can translate them into this case by a linear transformation), and denote them by <span class="mathjax-tex">\(L_{1}\)</span>, <span class="mathjax-tex">\(L_{2}\)</span>, where <span class="mathjax-tex">\(L_{j}\)</span> can be expressed by <span class="mathjax-tex">\(\zeta=x+il_{j}\)</span> (<span class="mathjax-tex">\(x\in(-\infty,\infty)\)</span>, <span class="mathjax-tex">\(l_{2}< l_{1}\)</span> are real numbers) and take the direction from left to right as the positive direction. Let <span class="mathjax-tex">\(L=L_{1}+L_{2}\)</span>.</p><p>We want to get functions <span class="mathjax-tex">\(\Phi(z)\)</span> and <span class="mathjax-tex">\(\Psi(z)\)</span> such that <span class="mathjax-tex">\(\Phi(z)\)</span> is analytic in <span class="mathjax-tex">\(\{\operatorname{Im} z>l_{1}\} \cup\{\operatorname{Im} z< l_{2}\}\)</span>, <span class="mathjax-tex">\(\Psi(z)\)</span> is analytic in <span class="mathjax-tex">\(\{z: l_{2} < \operatorname{Im} z < l_{1}\}\)</span>, and we have the following boundary value conditions: </p><div id="Equ1" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$ \begin{cases} \Phi^{+}(\zeta)=D_{1}(\zeta)\Psi^{-}(\zeta)+G_{1}(\zeta), \quad \mbox{when }\zeta\in L_{1}, \\ \Phi^{-}(\zeta)=D_{2}(\zeta)\Psi^{+}(\zeta)+G_{2}(\zeta), \quad \mbox{when }\zeta\in L_{2}, \end{cases} $$</span></div><div class="c-article-equation__number"> (2.1) </div></div><p> where <span class="mathjax-tex">\(L_{j}\)</span>: <span class="mathjax-tex">\(\zeta=x+il_{j}\)</span> (<span class="mathjax-tex">\(j=1,2\)</span>), <span class="mathjax-tex">\(x\in(-\infty, \infty)\)</span>.</p><p>Actually, (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/10.1186/s13661-015-0301-0#Equ1">2.1</a>) is a boundary value problem on two parallel straight lines <span class="mathjax-tex">\(\operatorname{Im} z=l_{1}\)</span>, <span class="mathjax-tex">\(\operatorname{Im} z=l_{2}\)</span> with ∞ as a pole. Here <span class="mathjax-tex">\(\Phi^{+}(\zeta )\)</span> is the boundary value of analytic function <span class="mathjax-tex">\(\Phi^{+}(z)\)</span> which is analytic in <span class="mathjax-tex">\(\{z: \operatorname{Im} z> l_{1}\}\)</span> and belongs to the class <span class="mathjax-tex">\(\{1\}\)</span> on <span class="mathjax-tex">\(L_{1}\)</span>, <span class="mathjax-tex">\(\Phi^{-}(\zeta)\)</span> is the boundary value of analytic function <span class="mathjax-tex">\(\Phi ^{-}(z)\)</span> which is analytic in <span class="mathjax-tex">\(\{z: \operatorname{Im} z< l_{2}\}\)</span> and belongs to the class <span class="mathjax-tex">\(\{1\}\)</span> on <span class="mathjax-tex">\(L_{2}\)</span>, and <span class="mathjax-tex">\(\Psi^{\pm}(\zeta)\)</span> is the boundary value of analytic function <span class="mathjax-tex">\(\Psi(z)\)</span> which is analytic in <span class="mathjax-tex">\(\{z: l_{2} <\operatorname{Im} z < l_{1}\} \)</span> and belongs to the class <span class="mathjax-tex">\(\{1\}\)</span> on <span class="mathjax-tex">\(L_{1}\)</span>, <span class="mathjax-tex">\(L_{2}\)</span>, respectively. The functions <span class="mathjax-tex">\(D_{1}(\zeta)\)</span> and <span class="mathjax-tex">\(D_{2}(\zeta)\)</span> belong to <span class="mathjax-tex">\(\hat{H}\)</span> on <span class="mathjax-tex">\(L_{1}\)</span>, <span class="mathjax-tex">\(L_{2}\)</span>, respectively. The functions <span class="mathjax-tex">\(G_{1}(\zeta)\)</span> and <span class="mathjax-tex">\(G_{2}(\zeta)\)</span> belong to the class <span class="mathjax-tex">\(\{1\}\)</span> on <span class="mathjax-tex">\(L_{1}\)</span>, <span class="mathjax-tex">\(L_{2}\)</span>, respectively. Hence, for the functions appearing in (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/10.1186/s13661-015-0301-0#Equ1">2.1</a>) the one-sided limits exist when <span class="mathjax-tex">\(x\rightarrow\infty\)</span> on <span class="mathjax-tex">\(L_{1}\)</span>, <span class="mathjax-tex">\(L_{2}\)</span>.</p><p>It can be seen from (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/10.1186/s13661-015-0301-0#Equ1">2.1</a>) that the order of <span class="mathjax-tex">\(\Phi(z)\)</span> is equal to that of <span class="mathjax-tex">\(\Psi(z)\)</span> at infinity. Therefore, if the orders of <span class="mathjax-tex">\(\Phi(z)\)</span> and <span class="mathjax-tex">\(\Psi(z)\)</span> are <i>m</i> at infinity, then such a problem can be denoted as <span class="mathjax-tex">\(R_{m}\)</span>. Actually, problem <span class="mathjax-tex">\(R_{0}\)</span> and problem <span class="mathjax-tex">\(R_{-1}\)</span> are often discussed. On the problem <span class="mathjax-tex">\(R_{0}\)</span>, both <span class="mathjax-tex">\(\Phi(\infty)\)</span> and <span class="mathjax-tex">\(\Psi(\infty)\)</span> are supposed to be finite and nonzero. On <span class="mathjax-tex">\(R_{-1}\)</span>, both <span class="mathjax-tex">\(\Phi(\infty)\)</span> and <span class="mathjax-tex">\(\Psi(\infty)\)</span> are assumed to be zero. Such a problem <i>R</i> is called regular if <span class="mathjax-tex">\(D_{j}(\zeta)\)</span> is not zero on <i>L</i>; otherwise, it is called irregular or of exception type.</p> <h3 class="c-article__sub-heading" id="FPar8">Remark 2.1</h3> <p>Since the positive direction of <span class="mathjax-tex">\(L_{j}\)</span> is the direction from left to right, when the observer moves from left to right on <span class="mathjax-tex">\(L_{j}\)</span>, the boundary values of left region of <span class="mathjax-tex">\(L_{j}\)</span> is positive boundary value, <i>i.e.</i>, the positive boundary value of <span class="mathjax-tex">\(\Phi(z)\)</span> is the boundary value above <span class="mathjax-tex">\(L_{1}\)</span>, and the negative boundary value of <span class="mathjax-tex">\(\Phi(z)\)</span> is ones below <span class="mathjax-tex">\(L_{2}\)</span>. The positive or negative boundary values of <span class="mathjax-tex">\(\Psi(z)\)</span> can be defined in a similar way.</p> </div></div></section><section data-title="Resolution"><div class="c-article-section" id="Sec3-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Sec3"><span class="c-article-section__title-number">3 </span>Resolution</h2><div class="c-article-section__content" id="Sec3-content"><p>We only consider problem <span class="mathjax-tex">\(R_{0}\)</span> in this paper. Hence, we assume <span class="mathjax-tex">\(\Phi (\infty)\)</span> and <span class="mathjax-tex">\(\Psi(\infty)\)</span> are finite and nonzero. For problem <span class="mathjax-tex">\(R_{m}\)</span>, similar arguments can be used. In this paper, we only consider the normal case, that is, <span class="mathjax-tex">\(D_{j}(\zeta)\)</span> (<span class="mathjax-tex">\(j=1,2\)</span>) does not have zeroes and poles on <span class="mathjax-tex">\(L_{j}\)</span>. For the irregular case, similar discussions also work (see Section 2.5 of Chapter 2 in [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 1" title="
					Lu, JK: Boundary Value Problems for Analytic Functions. World Scientific, Singapore (2004)
				" href="/articles/10.1186/s13661-015-0301-0#ref-CR1" id="ref-link-section-d243226627e4697">1</a>]). Equation (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/10.1186/s13661-015-0301-0#Equ1">2.1</a>) can be written as </p><div id="Equ2" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$ \begin{cases} \Phi^{+}(\zeta)=D_{1}(\zeta)\Psi^{-}(\zeta)+G_{1}(\zeta),\quad \mbox{when }\zeta\in L_{1}, \\ \Psi^{+}(\zeta)=\frac{1}{D_{2}(\zeta)}\Phi^{-}(\zeta)-\frac{G_{2}(\zeta )}{D_{2}(\zeta)},\quad \mbox{when }\zeta\in L_{2}. \end{cases} $$</span></div><div class="c-article-equation__number"> (3.1) </div></div><p> In order to unify, let <span class="mathjax-tex">\(C_{1}(\zeta)=G_{1}(\zeta)\)</span>, <span class="mathjax-tex">\(C_{2}(\zeta)=G_{2}(\zeta )/D_{2}(\zeta)\)</span>, and the above equation can be transformed into </p><div id="Equ3" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$ \begin{cases} \Phi^{+}(\zeta)=D_{1}(\zeta)\Psi^{-}(\zeta)+C_{1}(\zeta),\quad \mbox{when }\zeta\in L_{1}, \\ \Psi^{+}(\zeta)=\frac{1}{D_{2}(\zeta)}\Phi^{-}(\zeta)-C_{2}(\zeta), \quad \mbox{when }\zeta \in L_{2}. \end{cases} $$</span></div><div class="c-article-equation__number"> (3.2) </div></div><p> By putting <span class="mathjax-tex">\(\kappa_{1}=\operatorname{Ind}_{L_{1}}D_{1}(\zeta)\)</span>, <span class="mathjax-tex">\(\kappa_{2}=\operatorname{Ind}_{L_{2}}D_{2}(\zeta )\)</span>, and <span class="mathjax-tex">\(\kappa=\sum_{j=1}^{2}\kappa_{j}\)</span>, we call <i>κ</i> as the index of problem (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/10.1186/s13661-015-0301-0#Equ1">2.1</a>). Without loss of generality, we take three points <span class="mathjax-tex">\(z_{0}\)</span>, <span class="mathjax-tex">\(z_{1}\)</span>, <span class="mathjax-tex">\(z_{2}\)</span> on the <i>Z</i> plane such that <span class="mathjax-tex">\(l_{1}< \operatorname{Im} z_{1}\)</span>, <span class="mathjax-tex">\(l_{2}<\operatorname{Im} z_{0}<l_{1}\)</span>, <span class="mathjax-tex">\(\operatorname{Im} z_{2}< l_{2}\)</span>. Then we take the following piecewise function: </p><div id="Equ4" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$ Y_{1}(z)= \begin{cases} e^{\Omega_{1}(z)} ,&\operatorname{Im} z>l_{1}, \\ (\frac{z-z_{0}}{z-z_{1}})^{k_{1}}e^{\Omega_{1}(z)}, &\operatorname{Im} z< l_{1}, \end{cases} \qquad Y_{2}(z)= \begin{cases} (\frac{z-z_{0}}{z-z_{2}})^{k_{2}}e^{\Omega_{2}(z)}, &\operatorname{Im} z>l_{2}, \\ e^{\Omega_{2}(z)},& \operatorname{Im} z<l_{2}, \end{cases} $$</span></div><div class="c-article-equation__number"> (3.3) </div></div><p> here <span class="mathjax-tex">\(\Omega_{j}(z)\)</span> (<span class="mathjax-tex">\(j=1,2\)</span>) is defined as follows: </p><div id="Equb" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$\Omega_{j}(z)=\frac{1}{\sqrt{2\pi}}\int_{il_{j}}^{+\infty +il_{j}}r_{j}(t)e^{itz} \, dt,\quad \mbox{when }l_{j}< \operatorname{Im} z_{j} $$</span></div></div><p> and </p><div id="Equc" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$\Omega_{j}(z)=\frac{1}{\sqrt{2\pi}}\int^{il_{j}}_{-\infty +il_{j}}r_{j}(t)e^{itz} \, dt,\quad \mbox{when }\operatorname{Im} z_{j} < l_{j}, $$</span></div></div><p> where </p><div id="Equd" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex"> $$\begin{aligned} \begin{aligned} &r_{1}(t)=\frac{1}{\sqrt{2\pi}}\int_{-\infty+il_{1}}^{+\infty+il_{1}} \log \tilde{D}_{1}(\tau)\cdot e^{-i\tau t}\, d\tau, \quad \tilde{D}_{1}(\tau)=\biggl(\frac{\tau -z_{0}}{\tau-z_{1}}\biggr)^{\kappa_{1}}D_{1}( \tau), \\ &r_{2}(t)=\frac{1}{\sqrt{2\pi}}\int_{-\infty+il_{2}}^{+\infty+il_{2}} \log \tilde{D}_{2}(\tau)\cdot e^{-i\tau t}\, d\tau, \quad \tilde{D}_{2}(\tau)=\biggl(\frac{\tau -z_{0}}{\tau-z_{2}}\biggr)^{\kappa_{2}}D_{2}^{-1}( \tau). \end{aligned} \end{aligned}$$ </span></div></div><p> The function <span class="mathjax-tex">\(\Omega_{j}(z)\)</span> defined above is analytic on the complex plane except <span class="mathjax-tex">\(L_{1}\)</span> and <span class="mathjax-tex">\(L_{2}\)</span>. The logarithmic function of the integrand has a certain analytic branch such that <span class="mathjax-tex">\(\log\frac {t-z_{0}}{t-z_{j}}|_{t=\infty}=0\)</span>; then <span class="mathjax-tex">\(Y_{j}^{+}(z)\)</span> and <span class="mathjax-tex">\(Y_{j}^{-}(z)\)</span> are analytic in <span class="mathjax-tex">\(\{z: \operatorname{Im} z>l_{j}\}\)</span> and <span class="mathjax-tex">\(\{z: \operatorname{Im} z< l_{j}\}\)</span>, respectively. Moreover, </p><div id="Eque" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$\frac{Y_{1}^{+}(t)}{Y_{1}^{-}(t)}=\biggl(\frac{t-z_{0}}{t-z_{1}}\biggr)^{-k_{1}}e^{\Omega _{1}^{+}(t)-\Omega_{1}^{-}(t)}= \biggl(\frac{t-z_{0}}{t-z_{1}}\biggr)^{-k_{1}} \exp\biggl\{ \frac{1}{\sqrt{2\pi}}\int _{-\infty+il_{1}}^{+\infty+il_{1}}r_{1}(\zeta )e^{it\zeta}\, d\zeta\biggr\} , $$</span></div></div><p> owing to </p><div id="Equf" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$V\bigl[r_{1}(t)\bigr]=\frac{1}{\sqrt{2\pi}}\int_{-\infty+il_{1}}^{+\infty +il_{1}}r_{1}( \zeta)e^{it\zeta}\, d\zeta, $$</span></div></div><p> by the representative of <span class="mathjax-tex">\(r_{1}(t)\)</span> as well as the relationship between Fourier transform and inverse Fourier transform, we have <span class="mathjax-tex">\(V[r_{1}(t)]=\log [(\frac{t-z_{0}}{t-z_{1}})^{k_{1}}D_{1}(t)]\)</span>, therefore </p><div id="Equ5" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$ \frac{Y_{1}^{+}(t)}{Y_{1}^{-}(t)}=\biggl(\frac{t-z_{0}}{t-z_{1}}\biggr)^{-k_{1}} \exp\biggl\{ \log\biggl[\biggl(\frac{t-z_{0}}{t-z_{1}}\biggr)^{k_{1}}D_{1}(t) \biggr]\biggr\} =D_{1}(t). $$</span></div><div class="c-article-equation__number"> (3.4) </div></div><p> Similarly, one has </p><div id="Equ6" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$ \frac{Y_{2}^{+}(t)}{Y_{2}^{-}(t)}=D_{2}^{-1}(t). $$</span></div><div class="c-article-equation__number"> (3.5) </div></div> <p>Putting (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/10.1186/s13661-015-0301-0#Equ5">3.4</a>), (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/10.1186/s13661-015-0301-0#Equ6">3.5</a>) into (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/10.1186/s13661-015-0301-0#Equ3">3.2</a>), we can obtain </p><div id="Equ7" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$ \begin{cases} \Phi^{+}(t)[Y_{1}^{+}(t)]^{-1}=\Psi ^{-}(t)[Y_{1}^{-}(t)]^{-1}+C_{1}(t)[Y_{1}^{+}(t)]^{-1},\quad t\in l_{1}, \\ \Psi^{+}(t)[Y_{2}^{+}(t)]^{-1}=\Phi ^{-}(t)[Y_{2}^{-}(t)]^{-1}-C_{2}(t)[Y_{2}^{+}(t)]^{-1},\quad t\in l_{2}. \end{cases} $$</span></div><div class="c-article-equation__number"> (3.6) </div></div><p> In (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/10.1186/s13661-015-0301-0#Equ7">3.6</a>), the first equality is multiplied by <span class="mathjax-tex">\([Y_{2}^{+}(t)]^{-1}\)</span>, the second one is multiplied by <span class="mathjax-tex">\([Y_{1}^{-}(t)]^{-1}\)</span>, then </p><div id="Equ8" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$ \begin{cases} \Phi^{+}(t)[Y_{1}^{+}(t)]^{-1}[Y_{2}^{+}(t)]^{-1} \\ \quad =\Psi ^{-}(t)[Y_{1}^{+}(t)]^{-1}[Y_{2}^{+}(t)]^{-1}+C_{1}(t)[Y_{1}^{+}(t)]^{-1}[Y_{2}^{+}(t)]^{-1},\quad t\in l_{1}, \\ \Psi^{+}(t)[Y_{2}^{+}(t)]^{-1}[Y_{1}^{-}(t)]^{-1} \\ \quad =\Phi ^{-}(t)[Y_{2}^{-}(t)]^{-1}[Y_{1}^{-}(t)]^{-1}-C_{2}(t)[Y_{2}^{+}(t)]^{-1}[Y_{1}^{-}(t)]^{-1},\quad t\in l_{2}, \end{cases} $$</span></div><div class="c-article-equation__number"> (3.7) </div></div><p> denoting </p><div id="Equ9" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$ F_{1}^{+}(z)=\frac{1}{\sqrt{2\pi}}\int_{il_{1}}^{+\infty+il_{1}}f_{1}( \tau )e^{i\tau z}\, d\tau, \qquad F_{1}^{-}(z)=-\frac{1}{\sqrt{2\pi}} \int^{il_{1}}_{-\infty +il_{1}}f_{1}(\tau)e^{i\tau z} \, d\tau, $$</span></div><div class="c-article-equation__number"> (3.8) </div></div><p> where </p><div id="Equg" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$f_{1}(t)=\frac{1}{\sqrt{2\pi}}\int_{-\infty+il_{1}}^{+\infty+il_{1}} \frac {C_{1}(\tau)}{Y_{1}^{+}(\tau)Y_{2}^{+}(\tau)}e^{-i\tau t}\, d\tau. $$</span></div></div><p> Using Lemma <a data-track="click" data-track-label="link" data-track-action="subsection anchor" href="/articles/10.1186/s13661-015-0301-0#FPar6">1.2</a>, we know that <span class="mathjax-tex">\(F_{1}^{+}(z)\)</span>, <span class="mathjax-tex">\(F_{1}^{-}(z)\)</span> are analytic in <span class="mathjax-tex">\(\operatorname{Im} z>l_{1}\)</span>, <span class="mathjax-tex">\(\operatorname{Im} z< l_{1}\)</span>, respectively. On <span class="mathjax-tex">\(L_{1}\)</span>, we have </p><div id="Equh" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$F^{+}_{1}(t)-F^{-}_{1}(t)=\frac{C_{1}(t)}{Y_{1}^{+}(t)Y_{2}^{+}(t)}. $$</span></div></div><p> Again we denote </p><div id="Equ10" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$ F_{2}^{+}(z)=\frac{1}{\sqrt{2\pi}}\int_{il_{2}}^{+\infty+il_{2}}f_{2}( \tau )e^{i\tau z}\, d\tau, \qquad F_{2}^{-}(z)=-\frac{1}{\sqrt{2\pi}}\int ^{il_{2}}_{-\infty +il_{2}}f_{2}(\tau)e^{i\tau z}\, d \tau, $$</span></div><div class="c-article-equation__number"> (3.9) </div></div><p> where </p><div id="Equi" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$f_{2}(t)=\frac{1}{\sqrt{2\pi}}\int_{-\infty+il_{2}}^{+\infty+il_{2}} \frac {C_{2}(\tau)}{Y_{1}^{-}(\tau)Y_{2}^{+}(\tau)}e^{-i\tau t}\, d\tau. $$</span></div></div><p> Similarly, <span class="mathjax-tex">\(F_{2}^{+}(z)\)</span>, <span class="mathjax-tex">\(F_{2}^{-}(z)\)</span> are analytic in <span class="mathjax-tex">\(\operatorname{Im} z>l_{2}\)</span>, <span class="mathjax-tex">\(\operatorname{Im} z< l_{2}\)</span>, respectively. On <span class="mathjax-tex">\(L_{2}\)</span>, we obtain </p><div id="Equj" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$F^{+}_{2}(t)-F^{-}_{2}(t)=\frac{C_{2}(t)}{Y_{1}^{-}(t)Y_{2}^{+}(t)}. $$</span></div></div><p> Then (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/10.1186/s13661-015-0301-0#Equ8">3.7</a>) may be reduced to </p><div id="Equ11" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$ \begin{cases} \Phi^{+}(t)[Y_{1}^{+}(t)Y_{2}^{+}(t)]^{-1}-F_{1}^{+}(t) \\ \quad =\Psi ^{-}(t)[Y_{1}^{-}(t)Y_{2}^{+}(t)]^{-1}-F_{1}^{-}(t),\quad t\in l_{1}, \\ \Psi^{+}(t)[Y_{1}^{-}(t)Y_{2}^{+}(t)]^{-1}+F_{2}^{-}(t) \\ \quad =\Phi ^{-}(t)[Y_{1}^{-}(t)Y_{2}^{-}(t)]^{-1}+F_{2}^{-}(t), \quad t\in l_{2}, \end{cases} $$</span></div><div class="c-article-equation__number"> (3.10) </div></div><p> in the two sides of the first equation of (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/10.1186/s13661-015-0301-0#Equ11">3.10</a>), by adding <span class="mathjax-tex">\(F_{2}^{+}(t)\)</span>; in the two sides of the second one by subtraction of <span class="mathjax-tex">\(F_{1}^{-}(t)\)</span>, we have </p><div id="Equ12" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$ \begin{cases} \Phi^{+}(t)[Y_{1}^{+}(t)Y_{2}^{+}(t)]^{-1}-F_{1}^{+}(t)+F_{2}^{+}(t) \\ \quad = \Psi ^{-}(t)[Y_{1}^{-}(t)Y_{2}^{+}(t)]^{-1}-F_{1}^{-}(t)+ F_{2}^{+}(t),\quad t\in l_{1}, \\ \Psi^{+}(t)[Y_{1}^{-}(t)Y_{2}^{+}(t)]^{-1}+F_{2}^{-}(t)-F_{1}^{-}(t) \\ \quad = \Phi ^{-}(t)[Y_{1}^{-}(t)Y_{2}^{-}(t)]^{-1}+F_{2}^{-}(t)-F_{1}^{-}(t),\quad t\in l_{2}, \end{cases} $$</span></div><div class="c-article-equation__number"> (3.11) </div></div><p> the left side of the first equation of (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/10.1186/s13661-015-0301-0#Equ12">3.11</a>) is denoted by <span class="mathjax-tex">\(M_{1}^{+}(t)\)</span>, the right side of one is denoted by <span class="mathjax-tex">\(M_{1}^{-}(t)\)</span>; the left side of the second equation of (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/10.1186/s13661-015-0301-0#Equ12">3.11</a>) is denoted by <span class="mathjax-tex">\(M_{2}^{+}(t)\)</span>, the right side of this one is denoted by <span class="mathjax-tex">\(M_{2}^{-}(t)\)</span>. Let </p><div id="Equ13" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$ M_{1}(z)= \begin{cases} M_{1}^{+}(z), &\operatorname{Im} z>l_{1}, \\ M_{1}^{-}(z),& \operatorname{Im} z< l_{1}, \end{cases} $$</span></div><div class="c-article-equation__number"> (3.12) </div></div><p> where </p><div id="Equk" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex"> $$\begin{aligned} \begin{aligned} &M_{1}^{+}(z)=\Phi^{+}(z)\bigl[Y_{1}^{+}(z)Y_{2}^{+}(z) \bigr]^{-1}-F_{1}^{+}(z)+F_{2}^{+}(z), \\ &M_{1}^{-}(z)=\Psi^{-}(z)\bigl[Y_{1}^{-}(z)Y_{2}^{+}(z) \bigr]^{-1}-F_{1}^{-}(z)+F_{2}^{+}(z). \end{aligned} \end{aligned}$$ </span></div></div> <p>(1) We firstly consider the solutions of <span class="mathjax-tex">\(M_{1}^{+}(z)\)</span> and <span class="mathjax-tex">\(M_{1}^{-}(z)\)</span>, respectively in <span class="mathjax-tex">\(\operatorname{Im} z>l_{1}\)</span> and <span class="mathjax-tex">\(\operatorname{Im} z< l_{1}\)</span>.</p><p>Case: <span class="mathjax-tex">\(k\geq0\)</span>.</p><p>Since <span class="mathjax-tex">\([Y_{1}^{+}(z)]^{-1}\)</span>, <span class="mathjax-tex">\([Y_{2}^{+}(z)]^{-1}\)</span> are analytic in <span class="mathjax-tex">\(\{z: \operatorname{Im} z>l_{1}\}\)</span>, <span class="mathjax-tex">\([Y_{1}^{+}(z)Y_{2}^{+}(z)]^{-1}\)</span> is analytic. It follows from <span class="mathjax-tex">\(F_{j}^{+}(z)\)</span> (<span class="mathjax-tex">\(j=1,2\)</span>) is analytic that <span class="mathjax-tex">\(M_{1}^{+}(z)\)</span> is analytic. Hence, the <span class="mathjax-tex">\(\lim_{z\rightarrow\infty\ (\operatorname{Im} z>l_{1})}M_{1}^{+}(z)\)</span> exists. Suppose that <span class="mathjax-tex">\(M_{1}^{+}(z)=H_{1}(z)\)</span>, then </p><div id="Equ14" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$ \Phi^{+}(z)=Y_{1}^{+}(z)Y_{2}^{+}(z) \bigl[F_{1}^{+}(z)-F_{2}^{+}(z)+H_{1}(z)\bigr], \quad \operatorname{Im} z>l_{1}, $$</span></div><div class="c-article-equation__number"> (3.13) </div></div><p> where <span class="mathjax-tex">\(H_{1}(z)\)</span> is analytic in <span class="mathjax-tex">\(\{z: \operatorname{Im} z>l_{1}\}\)</span> and the <span class="mathjax-tex">\(\lim_{z\rightarrow\infty\ (\operatorname{Im} z>l_{1})}H_{1}(z)\)</span> exists.</p><p>When <span class="mathjax-tex">\(\operatorname{Im} z< l_{1}\)</span>, since <span class="mathjax-tex">\(\Psi^{-}(z)\)</span> is defined in <span class="mathjax-tex">\(\{z: l_{2}<\operatorname{Im} z<l_{1}\}\)</span>, <span class="mathjax-tex">\(z_{0}\)</span> is a <i>k</i>-order pole of <span class="mathjax-tex">\([Y_{1}^{-}(z)Y_{2}^{+}(z)]^{-1}\)</span> (<span class="mathjax-tex">\(k>0\)</span>). In order to ensure that <span class="mathjax-tex">\(M_{1}^{-}(z)\)</span> is bounded at a pole <span class="mathjax-tex">\(z_{0}\)</span>, we can multiply by a factor <span class="mathjax-tex">\((z-z_{0})^{k}\)</span>. Thus, it has a <i>k</i>-order at <span class="mathjax-tex">\(z=\infty\)</span>, <i>i.e.</i>, we have a polynomial with <i>k</i> degree. Let <span class="mathjax-tex">\((z-z_{0})^{k}M_{1}^{-}(z)=p_{k}(z)\)</span>, hence, <span class="mathjax-tex">\(M_{1}^{-}(z)=\frac{p_{k}(z)}{(z-z_{0})^{k}}\)</span>, <i>i.e.</i>, </p><div id="Equ15" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$ \Psi^{-}(z)\bigl[Y_{1}^{-}(z)Y_{2}^{+}(z) \bigr]^{-1}-F_{1}^{-}(z)+F_{2}^{+}(z)= \frac {p_{k}(z)}{(z-z_{0})^{k}},\quad \operatorname{Im} z< l_{1}, $$</span></div><div class="c-article-equation__number"> (3.14) </div></div><p> where <span class="mathjax-tex">\(p_{k}(z)=C_{0}+C_{1}(z-z_{0})+\cdots+C_{k}(z-z_{0})^{k}\)</span> is a polynomial with degree no more than <i>κ</i>.</p><p>Case: <span class="mathjax-tex">\(k<0\)</span>.</p><p>It follows from similar arguments as above that <span class="mathjax-tex">\(M_{1}^{+}(z)\)</span> is analytic in <span class="mathjax-tex">\(\{z: \operatorname{Im} z>l_{1}\}\)</span>.</p><p>Because <span class="mathjax-tex">\([Y_{1}^{-}(z)Y_{2}^{+}(z)]^{-1}\)</span>, <span class="mathjax-tex">\(F_{1}^{-}(z)\)</span> and <span class="mathjax-tex">\(F_{2}^{+}(z)\)</span> are analytic in <span class="mathjax-tex">\(\{z: \operatorname{Im} z< l_{1}\}\)</span>, so is <span class="mathjax-tex">\(M_{1}^{-}(z)\)</span>. Moreover, <span class="mathjax-tex">\(M_{1}^{+}(t)=M_{1}^{-}(t)\)</span> on <span class="mathjax-tex">\(L_{1}\)</span>. Hence, <span class="mathjax-tex">\(M_{1}(z)\)</span> is holomorphic in the whole complex plane and the <span class="mathjax-tex">\(\lim_{z\rightarrow\infty} M_{1}(z)\)</span> exists. By the Liouville theorem and the principle of analytic continuation, there is a constant <i>C</i> such that <span class="mathjax-tex">\(M_{1}(z)=C\)</span>, and one has </p><div id="Equ16" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex"> $$\begin{aligned}& \Psi^{-}(z)=Y_{1}^{-}(z)Y_{2}^{+}(z)\bigl[F_{1}^{-}(z)-F_{2}^{+}(z)+C \bigr], \quad \operatorname{Im} z< l_{1}, \end{aligned}$$ </span></div><div class="c-article-equation__number"> (3.15) </div></div> <div id="Equ17" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex"> $$\begin{aligned}& \Phi^{-}(z)=Y_{1}^{+}(z)Y_{2}^{+}(z)\bigl[F_{1}^{+}(z)-F_{2}^{+}(z)+C \bigr],\quad \operatorname{Im} z>l_{1}. \end{aligned}$$ </span></div><div class="c-article-equation__number"> (3.16) </div></div><p> Noticing that <span class="mathjax-tex">\(z=z_{0}\)</span> is a pole of <span class="mathjax-tex">\(Y_{1}^{-}(z)Y_{2}^{+}(z)\)</span> with order −<i>k</i>, <span class="mathjax-tex">\(\Psi^{-}(z)\)</span> has a singularity at <span class="mathjax-tex">\(z_{0}\)</span>. In order to ensure that <span class="mathjax-tex">\(\Psi ^{-}(z)\)</span> is analytic in <span class="mathjax-tex">\(\{z: \operatorname{Im} z< l_{1}\}\)</span> (in fact, for solving <span class="mathjax-tex">\(\Psi ^{-}(z)\)</span> in the range that <span class="mathjax-tex">\(\operatorname{Im} z< l_{1}\)</span>, we should only consider the case that <span class="mathjax-tex">\(l_{2}< \operatorname{Im} z<l_{1}\)</span>). For the case that <span class="mathjax-tex">\(k=-1\)</span>, it is sufficient to eliminate the singularity by putting <span class="mathjax-tex">\(C=F_{2}^{+}(z_{0})-F_{1}^{-}(z_{0})\)</span>, then one can define <span class="mathjax-tex">\(\Psi^{-}(z)\)</span> in the following way: </p><div id="Equ18" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$ \Psi^{-}(z)=Y_{1}^{-}(z)Y_{2}^{+}(z) \bigl[F_{1}^{-}(z)-F_{2}^{+}(z)+F_{2}^{+}(z_{0})-F_{1}^{-}(z_{0}) \bigr]. $$</span></div><div class="c-article-equation__number"> (3.17) </div></div><p> When <span class="mathjax-tex">\(\kappa\leq-2\)</span>, such a <i>C</i> still cannot eliminate the singularity of <span class="mathjax-tex">\(\Psi^{-}(z)\)</span> at <span class="mathjax-tex">\(z=z_{0}\)</span>. But the following condition should be satisfied: </p><div id="Equl" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$F_{2}^{+(q)}(z_{0})-F_{1}^{-(q)}(z_{0})=0, \quad q=1,2,\ldots,-\kappa-1, $$</span></div></div><p> <i>i.e.</i>, </p><div id="Equ19" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$ \int_{-\infty+il_{1}}^{il_{1}}\tau^{q} f_{1}(\tau)e^{i\tau z_{0}}\, d\tau+\int^{+\infty+il_{2}}_{il_{2}} \tau^{q} f_{2}(\tau)e^{i\tau z_{0}}\, d\tau=0, \quad q=1,2, \ldots , -\kappa-1; $$</span></div><div class="c-article-equation__number"> (3.18) </div></div><p> (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/10.1186/s13661-015-0301-0#Equ16">3.15</a>) is a solution of (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/10.1186/s13661-015-0301-0#Equ1">2.1</a>) if and only if (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/10.1186/s13661-015-0301-0#Equ19">3.18</a>) holds. Therefore, </p><div id="Equ20" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex"> $$\begin{aligned}& \mbox{as }k>0,\quad \Psi^{-}(z)=Y_{1}^{-}(z)Y_{2}^{+}(z) \biggl[F_{1}^{-}(z)-F_{2}^{+}(z)+\frac {p_{k}(z)}{(z-z_{0})^{k}}\biggr],\quad \operatorname{Im} z< l_{1}, \end{aligned}$$ </span></div><div class="c-article-equation__number"> (3.19) </div></div> <div id="Equ21" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex"> $$\begin{aligned}& \Phi^{+}(z)=Y_{1}^{+}(z)Y_{2}^{+}(z)\bigl[F_{1}^{+}(z)-F_{2}^{+}(z)+H_{1}(z) \bigr], \quad \operatorname{Im} z>l_{1}, \end{aligned}$$ </span></div><div class="c-article-equation__number"> (3.20) </div></div> <div id="Equ22" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex"> $$\begin{aligned}& \mbox{as }k< 0,\quad \Psi^{-}(z)=Y_{1}^{-}(z)Y_{2}^{+}(z) \bigl[F_{1}^{-}(z)-F_{2}^{+}(z)+C\bigr],\quad \operatorname{Im} z<l_{1}, \end{aligned}$$ </span></div><div class="c-article-equation__number"> (3.21) </div></div> <div id="Equ23" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex"> $$\begin{aligned}& \Phi^{+}(z)=Y_{1}^{+}(z)Y_{2}^{+}(z)\bigl[F_{1}^{+}(z)-F_{2}^{+}(z)+C \bigr],\quad \operatorname{Im} z>l_{1}. \end{aligned}$$ </span></div><div class="c-article-equation__number"> (3.22) </div></div><p> However, the solvability conditions should be satisfied (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/10.1186/s13661-015-0301-0#Equ19">3.18</a>) for <span class="mathjax-tex">\(k<-1\)</span>. Similarly, we can define the following piecewise function: </p><div id="Equ24" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$ M_{2}(z)= \begin{cases} M_{2}^{+}(z),& \operatorname{Im} z>l_{2}, \\ M_{2}^{-}(z),& \operatorname{Im} z< l_{2}, \end{cases} $$</span></div><div class="c-article-equation__number"> (3.23) </div></div><p> where </p><div id="Equ25" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex"> $$\begin{aligned}& M_{2}^{+}(z)=\Psi^{+}(z)\bigl[Y_{1}^{-}(z)Y_{2}^{+}(z) \bigr]^{-1}-F_{1}^{-}(z)+F_{2}^{-}(z), \end{aligned}$$ </span></div><div class="c-article-equation__number"> (3.24) </div></div> <div id="Equ26" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex"> $$\begin{aligned}& M_{2}^{-}(z)=\Phi^{-}(z)\bigl[Y_{1}^{-}(z)Y_{2}^{-}(z) \bigr]^{-1}-F_{1}^{-}(z)+F_{2}^{-}(z). \end{aligned}$$ </span></div><div class="c-article-equation__number"> (3.25) </div></div> <p>(2) We secondly consider the solutions of <span class="mathjax-tex">\(M_{2}^{+}(z)\)</span> and <span class="mathjax-tex">\(M_{2}^{-}(z)\)</span>, respectively, in <span class="mathjax-tex">\(\operatorname{Im} z>l_{2}\)</span> and <span class="mathjax-tex">\(\operatorname{Im} z< l_{2}\)</span>.</p><p>Case: <span class="mathjax-tex">\(k \geq0\)</span>.</p><p>Since <span class="mathjax-tex">\(Y_{1}^{-}(z)\)</span> and <span class="mathjax-tex">\(Y_{2}^{-}(z)\)</span> are analytic in <span class="mathjax-tex">\(\{z: \operatorname{Im} z< l_{2}\}\)</span>, so is <span class="mathjax-tex">\([Y_{1}^{-}(z)Y_{2}^{-}(z)]^{-1}\)</span>. It follows from <span class="mathjax-tex">\(F_{j}^{-}(z)\)</span> (<span class="mathjax-tex">\(j=1,2\)</span>) being analytic that <span class="mathjax-tex">\(M_{2}^{-}(z)\)</span> is analytic. Hence, the <span class="mathjax-tex">\(\lim_{z\rightarrow \infty\ (\operatorname{Im} z< l_{2})}M_{2}^{-}(z)\)</span> exists. Suppose that <span class="mathjax-tex">\(M_{2}^{-}(z)=H_{2}(z)\)</span>, then </p><div id="Equ27" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$ \Phi^{-}(z)=Y_{1}^{-}(z)Y_{2}^{-}(z) \bigl[F_{1}^{-}(z)-F_{2}^{-}(z)+H_{2}(z)\bigr], $$</span></div><div class="c-article-equation__number"> (3.26) </div></div><p> where <span class="mathjax-tex">\(H_{2}(z)\)</span> is analytic in <span class="mathjax-tex">\(\{z: \operatorname{Im} z< l_{2}\}\)</span> and the <span class="mathjax-tex">\(\lim_{z\rightarrow\infty\ (\operatorname{Im} z< l_{2})}H_{2}(z)\)</span> exists.</p><p>When <span class="mathjax-tex">\(\operatorname{Im} z>l_{2}\)</span>, <span class="mathjax-tex">\(z=z_{0}\)</span> is a <i>k</i>-order pole of <span class="mathjax-tex">\([Y_{1}^{-}(z)Y_{2}^{+}(z)]^{-1}\)</span> (<span class="mathjax-tex">\(k>0\)</span>), then <span class="mathjax-tex">\(z=z_{0}\)</span> is a <i>k</i>-order pole of <span class="mathjax-tex">\(M_{2}^{+}(z)\)</span>. By similar arguments to above, one has </p><div id="Equ28" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$ \Psi^{+}(z)\bigl[Y_{1}^{-}(z)Y_{2}^{+}(z) \bigr]^{-1}-F_{1}^{-}(z)+F_{2}^{+}(z)= \frac{p_{k}(z)}{(z-z_{0})^{k}}. $$</span></div><div class="c-article-equation__number"> (3.27) </div></div> <p>Case: <span class="mathjax-tex">\(k<0\)</span>.</p><p>Since <span class="mathjax-tex">\([Y_{1}^{-}(z)Y_{2}^{-}(z)]^{-1}\)</span> has no singularity in <span class="mathjax-tex">\(\{z: \operatorname{Im} z< l_{2}\} \)</span>, <span class="mathjax-tex">\(M_{2}^{-}(z)\)</span> is analytic in <span class="mathjax-tex">\(\{z: \operatorname{Im} z< l_{2}\}\)</span>. Noticing that <span class="mathjax-tex">\([Y_{1}^{-}(z)Y_{2}^{+}(z)]^{-1}\)</span> is analytic in <span class="mathjax-tex">\(\{z: \operatorname{Im} z>l_{2}\}\)</span>, one finds that <span class="mathjax-tex">\(M_{2}^{+}(z)\)</span> is analytic in <span class="mathjax-tex">\(\{z: \operatorname{Im} z>l_{2}\}\)</span> and <span class="mathjax-tex">\(M_{2}^{+}(t)=M_{2}^{-}(t)\)</span> on <span class="mathjax-tex">\(L_{2}\)</span>. Therefore, <span class="mathjax-tex">\(M_{2}(z)\)</span> is holomorphic in the whole complex plane and the <span class="mathjax-tex">\(\lim_{z\rightarrow\infty}M_{2}(z)\)</span> exists. By similar arguments to (1), there exists a constant <i>C</i>, such that <span class="mathjax-tex">\(M_{2}(z)=C\)</span> and </p><div id="Equ29" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$ \begin{aligned} &\Psi^{+}(z)=Y_{1}^{-}(z)Y_{2}^{+}(z) \bigl[F_{1}^{-}(z)-F_{2}^{+}(z)+C\bigr],\quad \operatorname{Im} z>l_{2}, \\ &\Phi^{-}(z)=Y_{1}^{+}(z)Y_{2}^{+}(z)\bigl[F_{1}^{+}(z)-F_{2}^{+}(z)+C \bigr],\quad \operatorname{Im} z< l_{2}. \end{aligned} $$</span></div><div class="c-article-equation__number"> (3.28) </div></div><p> Moreover, (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/10.1186/s13661-015-0301-0#Equ19">3.18</a>) is also a necessary condition for solvability. Hence, </p><div id="Equ30" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex"> $$\begin{aligned}& \mbox{as }k>0,\quad \Psi^{+}(z)=Y_{1}^{-}(z)Y_{2}^{+}(z) \biggl[F_{1}^{-}(z)-F_{2}^{+}(z)+\frac{p_{k}(z)}{(z-z_{0})^{k}} \biggr], \end{aligned}$$ </span></div><div class="c-article-equation__number"> (3.29) </div></div> <div id="Equ31" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex"> $$\begin{aligned}& \Phi^{-}(z)=Y_{1}^{-}(z)Y_{2}^{-}(z)\bigl[F_{1}^{-}(z)-F_{2}^{-}(z)+H_{2}(z) \bigr], \end{aligned}$$ </span></div><div class="c-article-equation__number"> (3.30) </div></div> <div id="Equ32" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex"> $$\begin{aligned}& \mbox{as }k< 0,\quad \Psi^{+}(z)=Y_{1}^{-}(z)Y_{2}^{+}(z) \bigl[F_{1}^{-}(z)-F_{2}^{+}(z)+C\bigr], \end{aligned}$$ </span></div><div class="c-article-equation__number"> (3.31) </div></div> <div id="Equ33" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex"> $$\begin{aligned}& \Phi^{-}(z)=Y_{1}^{+}(z)Y_{2}^{+}(z)\bigl[F_{1}^{+}(z)-F_{2}^{+}(z)+C \bigr]. \end{aligned}$$ </span></div><div class="c-article-equation__number"> (3.32) </div></div> <p>Collecting results, for <span class="mathjax-tex">\(k\geq0\)</span> and <span class="mathjax-tex">\(l_{2}<\operatorname{Im} z< l_{1}\)</span>, one has </p><div id="Equ34" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$ \Psi(z)=Y_{1}^{-}(z)Y_{2}^{+}(z) \biggl[F_{1}^{-}(z)-F_{2}^{+}(z)+\frac{p_{k}(z)}{(z-z_{0})^{k}}\biggr], $$</span></div><div class="c-article-equation__number"> (3.33) </div></div><p> and, for <span class="mathjax-tex">\(k< 0 \)</span> and <span class="mathjax-tex">\(l_{2}< \operatorname{Im} z<l_{1}\)</span>, </p><div id="Equ35" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$ \Psi(z)=Y_{1}^{-}(z)Y_{2}^{+}(z) \bigl[F_{1}^{-}(z)-F_{2}^{+}(z)+C\bigr], $$</span></div><div class="c-article-equation__number"> (3.34) </div></div><p> where <span class="mathjax-tex">\(p_{k}(z)\)</span> and <i>C</i> as above. For <span class="mathjax-tex">\(z\in\{z: \operatorname{Im} z>l_{1}\}\)</span>, </p><div id="Equ36" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$ \Phi^{+}(z)=Y_{1}^{+}(z)Y_{2}^{+}(z) \bigl[F_{1}^{+}(z)-F_{2}^{+}(z)+H_{1}(z)\bigr], $$</span></div><div class="c-article-equation__number"> (3.35) </div></div><p> where <span class="mathjax-tex">\(H_{1}(z)\)</span> is analytic in <span class="mathjax-tex">\(\{z: \operatorname{Im} z>l_{1}\}\)</span> as <span class="mathjax-tex">\(k\geq0\)</span> and the <span class="mathjax-tex">\(\lim_{z\rightarrow\infty\ (\operatorname{Im} z>l_{1})}H_{1}(z)\)</span> exists. When <span class="mathjax-tex">\(k<0\)</span>, <span class="mathjax-tex">\(H_{1}(z)\equiv C\)</span> (constant). For <span class="mathjax-tex">\(z\in\{z: \operatorname{Im} z< l_{2}\}\)</span>, </p><div id="Equ37" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$ \Phi^{-}(z)=Y_{1}^{-}(z)Y_{2}^{-}(z) \bigl[F_{1}^{-}(z)-F_{2}^{-}(z)+H_{2}(z)\bigr], $$</span></div><div class="c-article-equation__number"> (3.36) </div></div><p> where <span class="mathjax-tex">\(H_{2}(z)\)</span> is analytic in <span class="mathjax-tex">\(\{z: \operatorname{Im} z< l_{2}\}\)</span> when <span class="mathjax-tex">\(k\geq0\)</span> and <span class="mathjax-tex">\(\lim_{z\rightarrow\infty\ (\operatorname{Im} z< l_{2})}H_{2}(z)\)</span> exists. <span class="mathjax-tex">\(H_{2}(z)\equiv C\)</span> (constant) when <span class="mathjax-tex">\(k<0\)</span>.</p><p>Hence we get the solution of the boundary value problem (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/10.1186/s13661-015-0301-0#Equ1">2.1</a>).</p> <h3 class="c-article__sub-heading" id="FPar9">Theorem 3.1</h3> <p> <i>The boundary value problem</i> (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/10.1186/s13661-015-0301-0#Equ2">3.1</a>) <i>with two unknown functions</i> <span class="mathjax-tex">\(\Psi(z)\)</span> <i>and</i> <span class="mathjax-tex">\(\Phi(z)\)</span> <i>on two parallel lines has a solution in</i> <span class="mathjax-tex">\(\{z: l_{2}< \operatorname{Im} z<l_{1}\}\)</span> <i>and</i> <span class="mathjax-tex">\(\{\operatorname{Im} z>l_{1}\}\cup\{\operatorname{Im} z< l_{2}\}\)</span>, <i>respectively</i>. <i>Moreover</i>, <i>the general solution can be expressed by</i> (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/10.1186/s13661-015-0301-0#Equ34">3.33</a>)-(<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/10.1186/s13661-015-0301-0#Equ37">3.36</a>), <i>where</i> <span class="mathjax-tex">\(Y_{j}^{\pm }(z)\)</span> (<span class="mathjax-tex">\(j=1,2\)</span>) <i>is defined by</i> (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/10.1186/s13661-015-0301-0#Equ4">3.3</a>) <i>and</i> <span class="mathjax-tex">\(F_{j}(z)\)</span> (<span class="mathjax-tex">\(j=1,2\)</span>) <i>are defined by</i> (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/10.1186/s13661-015-0301-0#Equ9">3.8</a>) <i>and</i> (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/10.1186/s13661-015-0301-0#Equ10">3.9</a>). <i>When</i> <span class="mathjax-tex">\(\kappa>-1\)</span>, <span class="mathjax-tex">\(p_{k}(z)\)</span> <i>is a polynomial with</i> <i>κ</i> <i>order</i>, <i>and when</i> <span class="mathjax-tex">\(\kappa\leq-1\)</span>, <i>the necessary conditions for solvability still are</i> (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/10.1186/s13661-015-0301-0#Equ19">3.18</a>). <i>In all</i>, <i>the degree of freedom of the solution is</i> <span class="mathjax-tex">\(\kappa+1\)</span>.</p> </div></div></section><section data-title="Further discussion on solution and solvability conditions"><div class="c-article-section" id="Sec4-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Sec4"><span class="c-article-section__title-number">4 </span>Further discussion on solution and solvability conditions</h2><div class="c-article-section__content" id="Sec4-content"><p>In this section, we say more about the solution (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/10.1186/s13661-015-0301-0#Equ34">3.33</a>)-(<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/10.1186/s13661-015-0301-0#Equ37">3.36</a>) of (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/10.1186/s13661-015-0301-0#Equ1">2.1</a>) and the solvability conditions.</p><p>(1) The case that the solution lies in <span class="mathjax-tex">\(\operatorname{Im} z>l_{1}\)</span> and <span class="mathjax-tex">\(\operatorname{Im} z< l_{2}\)</span>.</p><p>As in (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/10.1186/s13661-015-0301-0#Equ28">3.27</a>) and (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/10.1186/s13661-015-0301-0#Equ29">3.28</a>), <span class="mathjax-tex">\(\Phi^{+}(z)\)</span> is analytic in <span class="mathjax-tex">\(\{z: \operatorname{Im} z> l_{1}\}\)</span> and <span class="mathjax-tex">\(\Phi^{-}(z)\)</span> is analytic in <span class="mathjax-tex">\(\{z: \operatorname{Im} z< l_{2}\}\)</span>. No matter how we choose <i>κ</i>, the boundary value problem (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/10.1186/s13661-015-0301-0#Equ1">2.1</a>) is solvable and its solution can be expressed by (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/10.1186/s13661-015-0301-0#Equ36">3.35</a>)-(<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/10.1186/s13661-015-0301-0#Equ37">3.36</a>).</p><p>(2) The case that the solution lies in <span class="mathjax-tex">\(l_{2}<\operatorname{Im} z<l_{1}\)</span>.</p><p>It can be seen from the expression of <span class="mathjax-tex">\(\Psi(z)\)</span> that <span class="mathjax-tex">\(z_{0}\)</span> is a <span class="mathjax-tex">\(|\kappa |\)</span>-order pole of <span class="mathjax-tex">\(Y_{1}^{-}(z)Y_{2}^{+}(z)\)</span> when <span class="mathjax-tex">\(\kappa<0\)</span>. In order to ensure (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/10.1186/s13661-015-0301-0#Equ1">2.1</a>) is solvable, one has <span class="mathjax-tex">\(C=F_{2}^{+}(z_{0})-F_{1}^{-}(z_{0})\)</span> when <span class="mathjax-tex">\(k=-1\)</span>, <i>i.e.</i>, </p><div id="Equ38" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$ C=\frac{1}{\sqrt{2\pi}}\int_{-\infty+il_{1}}^{il_{1}}f_{1}( \tau)e^{i\tau z_{0}}\, d\tau+\frac{1}{\sqrt{2\pi}}\int_{il_{2}}^{+\infty+il_{2}}f_{2}( \tau )e^{i\tau z_{0}}\, d\tau. $$</span></div><div class="c-article-equation__number"> (4.1) </div></div> <p>When <span class="mathjax-tex">\(k<-1\)</span>, the following <span class="mathjax-tex">\(|\kappa|-1\)</span> conditions are required: </p><div id="Equ39" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$ \int_{-\infty+il_{1}}^{il_{1}}\tau^{q} f_{1}(\tau)e^{i\tau z_{0}}\,d\tau+\int^{+\infty+il_{2}}_{il_{2}} \tau^{q} f_{2}(\tau)e^{i\tau z_{0}}\,d\tau=0, \quad q=1,2, \ldots ,-\kappa-1. $$</span></div><div class="c-article-equation__number"> (4.2) </div></div> <p>Then <span class="mathjax-tex">\(\Psi(z)\)</span> is analytic in <span class="mathjax-tex">\(\{z: l_{2}<\operatorname{Im} z<l_{1}\}\)</span> and has a bounded solution. When <span class="mathjax-tex">\(\kappa>0\)</span>, <span class="mathjax-tex">\(z_{0}\)</span> is a <i>κ</i>-order pole of <span class="mathjax-tex">\(Y_{1}^{-}(z)Y_{2}^{+}(z)\)</span>, and therefore <span class="mathjax-tex">\(Y_{1}^{-}(z)Y_{2}^{+}(z)\frac{p_{\kappa }(z)}{(z-z_{0})^{\kappa}}\)</span> is analytic in <span class="mathjax-tex">\(\{z: l_{2}<\operatorname{Im} z< l_{1}\}\)</span>. Hence, <span class="mathjax-tex">\(\Psi(z)\)</span> is analytic in <span class="mathjax-tex">\(\{z: l_{2}<\operatorname{Im} z<l_{1}\}\)</span> and <span class="mathjax-tex">\(\Psi(z)\)</span> is a constant while <span class="mathjax-tex">\(z=\infty\)</span>.</p><p>For <span class="mathjax-tex">\(z\in\{z: l_{2}< \operatorname{Im} z< l_{1}\}\)</span>, <span class="mathjax-tex">\(\Psi(z)\)</span> can be defined by (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/10.1186/s13661-015-0301-0#Equ34">3.33</a>), (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/10.1186/s13661-015-0301-0#Equ35">3.34</a>) if <span class="mathjax-tex">\(D_{1}(z)\)</span> and <span class="mathjax-tex">\(D_{2}^{-1}(z)\)</span> are not zero. Otherwise, if <span class="mathjax-tex">\(z_{1}^{*},z_{2}^{*},\ldots,z_{n}^{*}\)</span> are common zero-points of <span class="mathjax-tex">\(D_{1}(z)\)</span> and <span class="mathjax-tex">\(D_{2}^{-1}(z)\)</span> with the orders <span class="mathjax-tex">\(s_{1},s_{2},\ldots,s_{n}\)</span>, respectively, then <span class="mathjax-tex">\(\Psi^{(j)}(z_{q}^{*})=0\)</span> (<span class="mathjax-tex">\(1\leq q\leq n\)</span>, <span class="mathjax-tex">\(1\leq j\leq s_{q}\)</span>). Let <span class="mathjax-tex">\(s=\sum_{q=1}^{n} s_{q}\)</span>. Then the following solvability conditions must be augmented.</p><p>As <span class="mathjax-tex">\(\kappa\geq0\)</span>, the following <span class="mathjax-tex">\(\kappa+1\)</span> element equations with unknown numbers <span class="mathjax-tex">\(c_{0},c_{1},\ldots,c_{\kappa}\)</span>: </p><div id="Equ40" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$ \biggl[\frac{p_{\kappa}(z)}{(z-z_{0})^{\kappa}}\biggr]^{(j)}_{z=z^{*}_{q}} = \frac {j!i^{j}}{\sqrt{2\pi}}\biggl[\int_{-\infty+il_{1}}^{il_{1}} \tau^{j} f_{1}(\tau)e^{i\tau z}\,d\tau+ \int ^{+\infty+il_{2}}_{il_{2}}\tau^{j} f_{2}( \tau)e^{i\tau z}\,d\tau\biggr]. $$</span></div><div class="c-article-equation__number"> (4.3) </div></div><p> As <span class="mathjax-tex">\(\kappa<0\)</span>, the following condition is required: </p><div id="Equ41" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$ \int_{-\infty+il_{1}}^{il_{1}}\tau^{j} f_{1}(\tau)e^{i\tau z}\,d\tau+ \int^{+\infty+il_{2}}_{il_{2}} \tau^{j} f_{2}(\tau)e^{i\tau z}\,d\tau=0 $$</span></div><div class="c-article-equation__number"> (4.4) </div></div><p> (<span class="mathjax-tex">\(j=0,1,2,\ldots,s_{q}\)</span>; <span class="mathjax-tex">\(q=1,2,\ldots,n\)</span>), where <span class="mathjax-tex">\(c_{0},c_{1},\ldots,c_{\kappa }\)</span> are the coefficients of <span class="mathjax-tex">\(p_{k}(z)\)</span>.</p><p>(3) The case of solutions at <span class="mathjax-tex">\(z=\infty\)</span>.</p><p>In order to discuss the solution at <span class="mathjax-tex">\(z=\infty\)</span>, we denote </p><div id="Equm" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex"> $$\begin{aligned}& \gamma_{\infty}^{(1)}=\mu_{\infty}^{(1)}+ i \nu_{\infty}^{(1)}=\frac {1}{2\pi i}\bigl\{ \log D_{1}(il_{1}+\infty)-\log D_{1}(il_{1}- \infty)\bigr\} , \\& \gamma_{\infty}^{(2)}=\mu_{\infty}^{(2)}+ i \nu_{\infty}^{(2)}=\frac {1}{2\pi i}\bigl\{ \log D_{2}(il_{2}+\infty)-\log D_{2}(il_{2}- \infty)\bigr\} , \\& \mu_{\infty}=\mu_{\infty}^{(1)}+\mu_{\infty}^{(2)}, \end{aligned}$$ </span></div></div><p> where the logarithm function <span class="mathjax-tex">\(\log D_{j}(\tau)\)</span> takes some certain continuous branch when <span class="mathjax-tex">\(\operatorname{Re} \zeta>0\)</span> or <span class="mathjax-tex">\(\operatorname{Re} \zeta<0\)</span> such that <span class="mathjax-tex">\(0\leq\mu _{\infty}<1\)</span>.</p><p>If <span class="mathjax-tex">\(z=\infty\)</span> is a common node, it follows from <span class="mathjax-tex">\(F_{j}(\infty)=0\)</span> (<span class="mathjax-tex">\(j=1,2\)</span>) that <span class="mathjax-tex">\(F_{j}(\zeta)=\frac{F_{j}^{*}(\zeta)}{|\zeta|^{\mu_{j}^{*}}}\)</span>, <span class="mathjax-tex">\(\mu_{j}^{*}< \mu _{\infty}^{(j)}\)</span> and <span class="mathjax-tex">\(F_{j}^{*}(\zeta)\in H\)</span> near <span class="mathjax-tex">\(z=\infty\)</span>. By the conditions of (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/10.1186/s13661-015-0301-0#Equ1">2.1</a>), one has <span class="mathjax-tex">\(\Psi(\zeta)\in\{1\}\)</span>. Therefore, <span class="mathjax-tex">\(\Psi (\infty)\)</span> exists and is finite. Denote <span class="mathjax-tex">\(F(\zeta)=F_{1}(\zeta)-F_{2}(\zeta )\)</span>. Note that <span class="mathjax-tex">\(0\leq\mu_{\infty}<1\)</span>. If <span class="mathjax-tex">\(\mu_{\infty}>\frac{1}{2}\)</span>, it is clear that <span class="mathjax-tex">\(Y_{1}^{-}(\zeta)Y_{2}^{+}(\zeta)F(\zeta)=O(1/|\zeta|^{\mu_{\infty }-\varepsilon})\)</span> (where <i>ε</i> is a positive number sufficiently small and <span class="mathjax-tex">\(|\zeta|\)</span> is large enough) and <span class="mathjax-tex">\(Y_{1}^{-}(\zeta)Y_{2}^{+}(\zeta)\frac {p_{\kappa}(\zeta)}{(\zeta-z_{0})^{\kappa}}=O(1)\)</span>. If <span class="mathjax-tex">\(\mu_{\infty}\leq \frac{1}{2}\)</span>, in order to ensure that <span class="mathjax-tex">\(\Psi(\zeta)\in\{1\}\)</span>, the coefficient <span class="mathjax-tex">\(e_{k}\)</span> of <span class="mathjax-tex">\(p_{k}(z)\)</span> should be taken as </p><div id="Equ42" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$ e_{k}=\frac{1}{\sqrt{2\pi}}\int_{-\infty+il_{1}}^{il_{1}}f_{1}( \tau)e^{i\tau z}\,d\tau -\frac{1}{\sqrt{2\pi}}\int^{+\infty+il_{2}}_{il_{2}}f_{2}( \tau)e^{i\tau z}\,d\tau,\quad \mbox{while }\kappa\geq0. $$</span></div><div class="c-article-equation__number"> (4.5) </div></div> <p>For <span class="mathjax-tex">\(\kappa<0\)</span>, the condition (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/10.1186/s13661-015-0301-0#Equ39">4.2</a>) should hold and <span class="mathjax-tex">\(j=1,2,\ldots ,|\kappa|\)</span>.</p><p>If <span class="mathjax-tex">\(z=\infty\)</span> is a special node, <i>i.e.</i>, <span class="mathjax-tex">\(\mu_{\infty}=0\)</span>, one can translate it into the case that <span class="mathjax-tex">\(\mu_{\infty}\leq\frac{1}{2}\)</span> as a common node. For the rest, similar arguments can be used [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 9" title="
					Li, PR: The integral equations containing both cosecant and convolution kernel with periodicity. J. Syst. Sci. Math. Sci. 30(8), 1148-1155 (2010)
				" href="/articles/10.1186/s13661-015-0301-0#ref-CR9" id="ref-link-section-d243226627e26114">9</a>].</p><p>As for the boundary value problem with <i>n</i> unknown functions on <i>n</i> (<span class="mathjax-tex">\(n>2\)</span>) parallel lines, there is no essential difference for the solving method with the case <span class="mathjax-tex">\(n=2\)</span>. We will not elaborate.</p></div></div></section><section data-title="Example"><div class="c-article-section" id="Sec5-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Sec5"><span class="c-article-section__title-number">5 </span>Example</h2><div class="c-article-section__content" id="Sec5-content"><p>In this section we consider one important example in practice. In (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/10.1186/s13661-015-0301-0#Equ3">3.2</a>), suppose </p><div id="Equn" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex"> $$\begin{aligned}& D_{1}(\zeta)=D_{2}(\zeta)=1,\qquad C_{1}( \zeta)=\frac{1}{1+\zeta^{2}},\qquad C_{2}(\zeta)=\frac{1}{2+\zeta^{2}}, \\& L_{1}\mbox{:}\quad \zeta=0, \qquad L_{2}\mbox{:}\quad \zeta=x+i\quad (-\infty< x<+\infty). \end{aligned}$$ </span></div></div><p> Without loss of generality, we assume that <span class="mathjax-tex">\(z_{1}=\frac{3i}{2}\)</span>, <span class="mathjax-tex">\(z_{2}=\frac{-i}{2}\)</span>, <span class="mathjax-tex">\(z_{0}=\frac{i}{2}\)</span>. Then we have <span class="mathjax-tex">\(\kappa_{1}=\kappa_{2}=0\)</span> and hence <span class="mathjax-tex">\(\kappa=0\)</span>. Therefore, <span class="mathjax-tex">\(\gamma_{j}(t)=0\)</span>, <span class="mathjax-tex">\(\Omega_{j}(t)=0 \)</span>, <span class="mathjax-tex">\(Y_{j}(z)=1\)</span> (<span class="mathjax-tex">\(j=1,2\)</span>). In this case, by (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/10.1186/s13661-015-0301-0#Equ9">3.8</a>) and (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/10.1186/s13661-015-0301-0#Equ10">3.9</a>), we obtain </p><div id="Equo" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex"> $$\begin{aligned}& f_{1}(t)=\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{+\infty} \frac{1}{1+\tau ^{2}}e^{-i\tau t}\,d\tau=\frac{\sqrt{\pi}{e}}{2}^{-t}, \\& f_{2}(t)=\frac{1}{\sqrt{2\pi}}\int_{-\infty+i}^{+\infty+i} \frac{1}{2+\tau ^{2}}e^{-i\tau t}\,d\tau=\frac{\sqrt{\pi}{e}}{2}^{-\sqrt{2}t}, \end{aligned}$$ </span></div></div><p> and then </p><div id="Equ43" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex"> $$\begin{aligned}& F_{1}^{+}(z)=\frac{1}{\sqrt{2\pi}}\int_{0}^{+\infty}f_{1}( \tau)e^{i\tau z}\,d\tau=\frac{i}{2\sqrt{2}(z+i)}, \end{aligned}$$ </span></div><div class="c-article-equation__number"> (5.1) </div></div> <div id="Equ44" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex"> $$\begin{aligned}& F_{1}^{-}(z)=-\frac{1}{\sqrt{2\pi}}\int^{0}_{-\infty }f_{1}( \tau)e^{i\tau z}\,d\tau=\frac{i}{2\sqrt{2}(z-i)}. \end{aligned}$$ </span></div><div class="c-article-equation__number"> (5.2) </div></div><p> Similarly, we have </p><div id="Equ45" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$ F_{2}^{+}(z)=\frac{i}{2\sqrt{2}(z+\sqrt{2}i)},\qquad F_{2}^{-}(z)=\frac{i}{2\sqrt{2}(z-\sqrt{2}i)}. $$</span></div><div class="c-article-equation__number"> (5.3) </div></div><p> Then we obtain the solutions of (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/10.1186/s13661-015-0301-0#Equ3">3.2</a>): </p><div id="Equ46" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex"> $$\begin{aligned}& \Psi(z)=\frac{i}{2\sqrt{2}(z-i)}-\frac{i}{2\sqrt{2}(z+\sqrt{2}i)}+ C,\quad \mbox{when }0< \operatorname{Im}<1, \\& \Phi^{+}(z)=\frac{i}{2\sqrt{2}(z+i)}-\frac{i}{2\sqrt{2}(z+\sqrt{2}i)}+ H_{1}(z), \quad \mbox{when }\operatorname{Im} z>1, \\& \Phi^{-}(z)=\frac{i}{2\sqrt{2}(z-i)}-\frac{i}{2\sqrt{2}(z-\sqrt{2}i)}+ H_{2}(z), \quad \mbox{when }\operatorname{Im} z<0, \end{aligned}$$ </span></div><div class="c-article-equation__number"> (5.4) </div></div><p> where <i>C</i> is a constant, <span class="mathjax-tex">\(H_{1}(z)=(1-\frac{\sqrt{2}}{2})\frac {1}{1+z^{2}}\)</span>, <span class="mathjax-tex">\(H_{2}(z)=0\)</span>.</p></div></div></section> <div id="MagazineFulltextArticleBodySuffix"><section aria-labelledby="Bib1" data-title="References"><div class="c-article-section" id="Bib1-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Bib1">References</h2><div class="c-article-section__content" id="Bib1-content"><div data-container-section="references"><ol class="c-article-references" data-track-component="outbound reference" data-track-context="references section"><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="1."><p class="c-article-references__text" id="ref-CR1"> Lu, JK: Boundary Value Problems for Analytic Functions. 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One class of generalized boundary value problem for analytic functions. <i>Bound Value Probl</i> <b>2015</b>, 40 (2015). https://doi.org/10.1186/s13661-015-0301-0</p><p class="c-bibliographic-information__download-citation u-hide-print"><a data-test="citation-link" data-track="click" data-track-action="download article citation" data-track-label="link" data-track-external="" rel="nofollow" href="https://citation-needed.springer.com/v2/references/10.1186/s13661-015-0301-0?format=refman&flavour=citation">Download citation<svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-download-medium"></use></svg></a></p><ul class="c-bibliographic-information__list" data-test="publication-history"><li class="c-bibliographic-information__list-item"><p>Received<span class="u-hide">: </span><span class="c-bibliographic-information__value"><time datetime="2014-08-05">05 August 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