Document Zbl 1173.34308

<!doctype html> <html lang="en"> <head> <meta charset="utf-8"> <title>Document Zbl 1173.34308 - zbMATH Open</title> <meta name="viewport" content="width=device-width, minimum-scale=0.1, maximum-scale=5.0"> <meta name="robots" content="noarchive, noindex"> <meta name="referrer" content="origin-when-cross-origin"> <link href="https://static.zbmath.org/contrib/bootstrap/v3.3.7/css/bootstrap.min.css" rel="stylesheet" media="screen,print"> <link href="https://static.zbmath.org/contrib/bootstrap/v3.3.7/css/bootstrap-theme.min.css" rel="stylesheet" media="screen,print"> <link href="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.css" rel="stylesheet" media="screen,print"> <link rel="stylesheet" href="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/css/bootstrap-select.min.css"> <link href="/static/css/smoothness/jquery-ui-1.10.1.custom.min.css" rel="stylesheet" media="screen"> <link href="/static/styles.css?v=20250402" rel="stylesheet" media="screen,print"> <link href="https://static.zbmath.org/zbMathJax/v0.1.38/zbmathjax.css" rel="stylesheet" media="screen,print"> <link rel="shortcut icon" href="/static/zbmath.ico"> <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "Organization", "url": "https://zbmath.org/", "logo": "https://zbmath.org/static/zbMATH.png" } </script> </head> <body> <div id="line"></div> <span id="clear" style="cursor: pointer;">×</span> <div id="page"> <div id="head"> <nav id="menu" class="navbar navbar-default"> <div class="container-fluid"> <div class="navbar-header"> <button type="button" class="navbar-toggle collapsed" data-toggle="collapse" data-target="#zbnav" aria-expanded="false"> <span class="sr-only">Toggle navigation</span> <span class="icon-bar"></span> <span class="icon-bar"></span> <span class="icon-bar"></span> </button> <a class="navbar-brand" href="#"> <img class="logo" src="/static/zbmath.gif" alt="zbMATH Open logo"> </a> </div> <div id="zbnav" class="collapse navbar-collapse"> <ul class="nav navbar-nav pages"> <li class="about"> <a href="/about/">About</a> </li> <li class="frequently-asked-questions"> <a href="/faq/">FAQ</a> </li> <li class="general-help"> <a href="/general-help/">General Help</a> </li> <li class="reviewer-service"> <a href="https://zbmath.org/reviewer-service/" target="_self" >Reviewer Service</a> </li> <li> <a href="/tools-and-resources/">Tools & Resources</a> </li> <li class="contact"> <a href="/contact/">Contact</a> </li> </ul> <ul class="nav navbar-nav navbar-right prefs"> <li class="preferences dropdown"> <a data-toggle="dropdown" href="#">Preferences <i class="caret"></i></a> <ul class="dropdown-menu preferences"> <li> <form id="preferences" class="navbar-form" method="post" action="/preferences/" onsubmit="return confirm('This website uses cookies for the purposes of storing preference information on your device. Do you agree to this?\n\nPlease refer to our Privacy Policy to learn more about our use of cookies.')" > <input type="hidden" name="path" value="/1173.34308?"> <span class=""> <label class="title">Search Form</label> <div class="form-group"> <input id="search-multi-line" type="radio" name="search" value="multi-line" checked> <label for="search-multi-line" class="radio">Multi-Line Search (default)</label> </div> <div class="form-group"> <input id="search-one-line" type="radio" name="search" value="one-line"> <label for="search-one-line" class="radio">One-Line Search</label> </div> </span> <span class="count"> <label class="title">Hits per Page</label> <div class="form-group"> <input id="count-10" type="radio" name="count" value="10"> <label for="count-10" class="radio">10</label> </div> <div class="form-group"> <input id="count-20" type="radio" name="count" value="20"> <label for="count-20" class="radio">20</label> </div> <div class="form-group"> <input id="count-50" type="radio" name="count" value="50"> <label for="count-50" class="radio">50</label> </div> <div class="form-group"> <input id="count-100" type="radio" name="count" value="100" checked> <label for="count-100" class="radio">100 (default)</label> </div> <div class="form-group"> <input id="count-200" type="radio" name="count" value="200"> <label for="count-200" class="radio">200</label> </div> </span> <span class="format"> <label class="title">Display Format</label> <div class="form-group"> <input id="format-mathjax" type="radio" name="format" value="mathjax" checked> <label for="format-mathjax" class="radio">MathJax (default)</label> </div> <div class="form-group"> <input id="format-amstex" type="radio" name="format" value="latex"> <label for="format-amstex" class="radio">LaTeX</label> </div> </span> <span class="ranking"> <label class="title">Documents Sorting</label> <div class="form-group"> <input id="documents-ranking-default" type="radio" name="documents_ranking" value="date" checked> <label for="documents-ranking-default" class="radio">Newest first (default)</label> </div> <div class="form-group"> <input id="documents-ranking-references" type="radio" name="documents_ranking" value="references"> <label for="documents-ranking-references" class="radio">Citations</label> </div> <div class="form-group"> <input id="documents-ranking-relevance" type="radio" name="documents_ranking" value="relevance"> <label for="documents-ranking-relevance" class="radio">Relevance</label> </div> </span> <span class="ranking"> <label class="title">Authors Sorting</label> <div class="form-group"> <input id="authors-ranking-default" type="radio" name="authors_ranking" value="alpha" checked> <label for="authors-ranking-default" class="radio">Alphabetically (default)</label> </div> <div class="form-group"> <input id="authors-ranking-references" type="radio" name="authors_ranking" value="references"> <label for="authors-ranking-references" class="radio">Citations</label> </div> </span> <span class="ranking"> <label class="title">Serials Sorting</label> <div class="form-group"> <input id="serials-ranking-default" type="radio" name="serials_ranking" value="alpha" checked> <label for="serials-ranking-default" class="radio">Alphabetically (default)</label> </div> <div class="form-group"> <input id="serials-ranking-references" type="radio" name="serials_ranking" value="references"> <label for="serials-ranking-references" class="radio">Citations</label> </div> </span> <span class="ranking"> <label class="title">Software Sorting</label> <div class="form-group"> <input id="software-ranking-default" type="radio" name="software_ranking" value="references" checked> <label for="software-ranking-default" class="radio">Citations (default)</label> </div> <div class="form-group"> <input id="software-ranking-alpha" type="radio" name="software_ranking" value="alpha"> <label for="software-ranking-alpha" class="radio">Alphabetically</label> </div> </span> <button type="submit" class="btn btn-default">OK</button> <div class="clearfix"> </form> </li> </ul> </li> </ul> </div> </div> </nav> <div id="tabs"> <h1 class="logo"> <a class="logo" href="/"> <img class="logo" src="/static/zbmath.gif" alt="zbMATH Open — the first resource for mathematics" > </a> </h1> <nav> <ul class="nav nav-tabs"> <li class="tab-documents active"> <a href="/">Documents</a> </li> <li class="tab-authors"> <a href="/authors/">Authors</a> </li> <li class="tab-serials"> <a href="/serials/">Serials</a> </li> <li class="tab-software"> <a href="/software/">Software</a> </li> <li class="tab-classification"> <a href="/classification/">Classification</a> </li> <li class="tab-formulae"> <a href="/formulae/">Formulæ</a> </li> </ul> </nav> <div class="clearfix"></div> </div> <div class="content-fixed"> <div class="content-formular"> <div style="display: none;"> <div class="row ml-0"id="multi-line-new-line" style="display: none;"> <div class="col-xs-12 form-inline multi-line"> <select class="form-control multi-line-field multi-line-selectpicker" name="ml-0-f" aria-label="field"> <option data-type="input" value="any" selected>Anywhere</option> <option data-type="input" value="au">Authors</option> <option data-type="input" value="ti">Title</option> <option data-type="input" value="py">Year</option> <option data-type="range" value="pyr">Year Range</option> <option data-type="input" value="cc">MSC</option> <option data-type="input" value="cc1">MSC Primary</option> <option data-type="input" value="so">Source / Journal</option> <option data-type="input" value="pu">Publisher</option> <option data-type="input" value="la">Language</option> <option data-type="input" value="ab">Summary / Review</option> <option data-type="input" value="rv">Reviewer</option> <option data-type="input" value="an">zbMATH ID</option> <option data-type="input" value="en">External ID</option> <option data-type="input" value="ut">Keywords</option> <option data-type="input" value="sw">Software</option> <option data-type="input" value="br">Biographic Ref</option> <option data-type="input" value="rft">Reference Text</option> <option data-type="multiselect-db" value="db">Database</option> <option data-divider="true"></option> <option data-function="remove-line" data-content='<span class="glyphicon glyphicon-minus" aria-hidden="true"></span> remove line' value="any">remove line</option> </select><input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value"><select class="form-control multi-line-operators multi-line-selectpicker" name="ml-0-op" aria-label="operator"> <option value="and" selected>AND</option> <option value="andnot">AND NOT</option> <option value="or">OR</option> </select></div> </div> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input"> <span class="multi-line-value" id="multi-line-type-range"><span style="padding-left: 5px;">from</span> <input name="ml-0-v1" class="form-control multi-line-input" type="text" value="" aria-label="value"> until <input name="ml-0-v2" class="form-control multi-line-input" type="text" value="" aria-label="value"></span> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-la" placeholder="use name or ISO code"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-rv" placeholder="enter name or zbMATH reviewer number"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-an" placeholder="Zbl, JFM or ERAM number"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-en" placeholder="e.g. DOI, ISBN, arXiv ID"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-sw" placeholder="use * to find all documents using software"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-br" placeholder="find documents about the life or work of a person"> <span class="multi-line-value" id="multi-line-type-multiselect-db"> <select class="multi-line-selectpicker" data-width="100%" multiple> <option value="zbl">Zbl</option> <option value="arxiv">arXiv</option> <option value="jfm">JFM</option> <option value="eram">ERAM</option> </select> <input type="hidden" class="multi-line-input" name="ml-0-v" value=""> </span> </div> <form name="documents" method="GET" action="/" autocomplete="off"> <div class="documents multi-line" style="display: none;"> <div class="forms"> <ul class="nav forms"> <li class="one-line"> <span tabindex="0" class="glyphicon glyphicon-question-sign" title="One-Line Search allows for free logical combinations of search fields" aria-label="One-Line Search allows for free logical combinations of search fields" data-placement="bottom"></span> <a style="display: inline-block;" href="#">One-Line Search <span class="glyphicon glyphicon-search"></span></a> </li> </ul> </div> <div class="clearfix"></div> <div class="container-fluid"> <input type="hidden" id="multi-line-ml" name="ml" value="3"> <div id="multi-line-row-wrapper"> <div class="row ml-1"> <div class="col-xs-12 form-inline multi-line"> <select class="form-control multi-line-field multi-line-selectpicker" name="ml-1-f" aria-label="field"> <option data-type="input" value="any" selected>Anywhere</option> <option data-type="input" value="au">Authors</option> <option data-type="input" value="ti">Title</option> <option data-type="input" value="py">Year</option> <option data-type="range" value="pyr">Year Range</option> <option data-type="input" value="cc">MSC</option> <option data-type="input" value="cc1">MSC Primary</option> <option data-type="input" value="so">Source / Journal</option> <option data-type="input" value="pu">Publisher</option> <option data-type="input" value="la">Language</option> <option data-type="input" value="ab">Summary / Review</option> <option data-type="input" value="rv">Reviewer</option> <option data-type="input" value="an">zbMATH ID</option> <option data-type="input" value="en">External ID</option> <option data-type="input" value="ut">Keywords</option> <option data-type="input" value="sw">Software</option> <option data-type="input" value="br">Biographic Ref</option> <option data-type="input" value="rft">Reference Text</option> <option data-type="multiselect-db" value="db">Database</option> <option data-divider="true"></option> <option data-function="remove-line" data-content='<span class="glyphicon glyphicon-minus" aria-hidden="true"></span> remove line' value="any">remove line</option> </select><input name="ml-1-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value"><select class="form-control multi-line-operators multi-line-selectpicker" name="ml-1-op" aria-label="operator"> <option value="and" selected>AND</option> <option value="andnot">AND NOT</option> <option value="or">OR</option> </select></div> </div> <div class="row ml-2"> <div class="col-xs-12 form-inline multi-line"> <select class="form-control multi-line-field multi-line-selectpicker" name="ml-2-f" aria-label="field"> <option data-type="input" value="any">Anywhere</option> <option data-type="input" value="au" selected>Authors</option> <option data-type="input" value="ti">Title</option> <option data-type="input" value="py">Year</option> <option data-type="range" value="pyr">Year Range</option> <option data-type="input" value="cc">MSC</option> <option data-type="input" value="cc1">MSC Primary</option> <option data-type="input" value="so">Source / Journal</option> <option data-type="input" value="pu">Publisher</option> <option data-type="input" value="la">Language</option> <option data-type="input" value="ab">Summary / Review</option> <option data-type="input" value="rv">Reviewer</option> <option data-type="input" value="an">zbMATH ID</option> <option data-type="input" value="en">External ID</option> <option data-type="input" value="ut">Keywords</option> <option data-type="input" value="sw">Software</option> <option data-type="input" value="br">Biographic Ref</option> <option data-type="input" value="rft">Reference Text</option> <option data-type="multiselect-db" value="db">Database</option> <option data-divider="true"></option> <option data-function="remove-line" data-content='<span class="glyphicon glyphicon-minus" aria-hidden="true"></span> remove line' value="any">remove line</option> </select><input name="ml-2-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value"><select class="form-control multi-line-operators multi-line-selectpicker" name="ml-2-op" aria-label="operator"> <option value="and" selected>AND</option> <option value="andnot">AND NOT</option> <option value="or">OR</option> </select></div> </div> <div class="row ml-3"> <div class="col-xs-12 form-inline multi-line"> <select class="form-control multi-line-field multi-line-selectpicker" name="ml-3-f" aria-label="field"> <option data-type="input" value="any">Anywhere</option> <option data-type="input" value="au">Authors</option> <option data-type="input" value="ti" selected>Title</option> <option data-type="input" value="py">Year</option> <option data-type="range" value="pyr">Year Range</option> <option data-type="input" value="cc">MSC</option> <option data-type="input" value="cc1">MSC Primary</option> <option data-type="input" value="so">Source / Journal</option> <option data-type="input" value="pu">Publisher</option> <option data-type="input" value="la">Language</option> <option data-type="input" value="ab">Summary / Review</option> <option data-type="input" value="rv">Reviewer</option> <option data-type="input" value="an">zbMATH ID</option> <option data-type="input" value="en">External ID</option> <option data-type="input" value="ut">Keywords</option> <option data-type="input" value="sw">Software</option> <option data-type="input" value="br">Biographic Ref</option> <option data-type="input" value="rft">Reference Text</option> <option data-type="multiselect-db" value="db">Database</option> <option data-divider="true"></option> <option data-function="remove-line" data-content='<span class="glyphicon glyphicon-minus" aria-hidden="true"></span> remove line' value="any">remove line</option> </select><input name="ml-3-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value"><div id="multi-line-plus"> <a href="#"><span class="glyphicon glyphicon-plus" aria-hidden="true"></span> add line</a> </div></div> </div> </div> <div class="row"> <div class="col-xs-12 form-inline"> <div class="form-group field checkboxes-wrapper" id="checkboxes-wrapper-test" style="visibility: hidden; position: fixed;"> <label>Document Type:</label> <div class="checkboxes"> <div class="slider"> <label title="search for Articles in Journals"> <input type="checkbox" class="form-control" value="j" checked> <span tabindex="0"><small></small></span> Journal Articles </label> </div> <div class="slider"> <label title="search for Articles in Conference Proceedings and Collected Volumes"> <input type="checkbox" class="form-control" value="a" checked> <span tabindex="0"><small></small></span> Collection Articles </label> </div> <div class="slider"> <label title="search for Monographs, Proceedings, Dissertations etc."> <input type="checkbox" class="form-control" value="b" checked> <span tabindex="0"><small></small></span> Books </label> </div> <div class="slider"> <label title="search for arXiv Preprints"> <input type="checkbox" class="form-control" value="p" checked> <span tabindex="0"><small></small></span> arXiv Preprints </label> </div> </div> </div> <div class="form-group field checkboxes-wrapper" id="checkboxes-wrapper-real"> <label>Document Type:</label> <div class="checkboxes"> <div class="slider"> <label for="dt-j" title="search for Articles in Journals"> <input type="checkbox" id="dt-j" name="dt" class="form-control" value="j" checked> <span tabindex="0"><small></small></span> Journal Articles </label> </div> <div class="slider"> <label for="dt-a" title="search for Articles in Conference Proceedings and Collected Volumes"> <input type="checkbox" id="dt-a" name="dt" class="form-control" value="a" checked> <span tabindex="0"><small></small></span> Collection Articles </label> </div> <div class="slider"> <label for="dt-b" title="search for Monographs, Proceedings, Dissertations etc."> <input type="checkbox" id="dt-b" name="dt" class="form-control" value="b" checked> <span tabindex="0"><small></small></span> Books </label> </div> <div class="slider"> <label for="dt-p" title="search for arXiv Preprints"> <input type="checkbox" id="dt-p" name="dt" class="form-control" value="p" checked> <span tabindex="0"><small></small></span> arXiv Preprints </label> </div> </div> </div> </div> </div> <div class="row"> <div class="col-xs-12 buttons"> <a tabindex="0" class="btn btn-default clear-all">Reset all <span class="glyphicon glyphicon-remove"></span></a> <div class="submit"> <button class="btn btn-default search" type="submit">Search <span class="glyphicon glyphicon-search"></span></button> </div> </div> </div> </div> </div> </form> <form class="form-inline" name="documents" method="GET" action="/"> <div class="documents one-line" style="display: block;"> <div class="forms"> <ul class="nav forms"> <li class="multi-line"><a href="#">New Multi-Line Search <span class="glyphicon glyphicon-list"></span></a></li> </ul> </div> <div id="search-row" class="input-group box"> <span> <div id="search-field"> <input class="query form-control" type="text" name="q" value="an:1173.34308" aria-label="Search for documents" placeholder="Search for documents" autocomplete="off"> </div> <div class="search-buttons input-group-btn"> <div class="btn-group"> <button class="btn btn-default search" type="submit"><span class="virtual">Search</span> <span class="glyphicon glyphicon-search" style="top: 2px;"></span></button> </div> </div> </span> <span> <div class="search-buttons input-group-btn"> <div class="btn-group"> <div class="btn-group fields"> <button class="btn btn-default dropdown-toggle" data-toggle="dropdown">Fields <i class="caret"></i></button> <ul id="fields" class="dropdown-menu pull-right"> <li><a href="#"><span class="token item">ab:</span><span>  </span>review text</a></li> <li><a href="#"><span class="token item">an:</span><span>  </span>zbmath id</a></li> <li><a href="#"><span class="token item">any:</span><span>  </span>anywhere</a></li> <li><a href="#"><span class="token item">au:</span><span>  </span>contributor name</a></li> <li><a href="#"><span class="token item">br:</span><span>  </span>biographic reference name</a></li> <li><a href="#"><span class="token item">cc:</span><span>  </span>msc title</a></li> <li><a href="#"><span class="token item">dt:</span><span>  </span>document type</a></li> <li><a href="#"><span class="token item">doi:</span><span>  </span>doi</a></li> <li><a href="#"><span class="token item">en:</span><span>  </span>external id</a></li> <li><a href="#"><span class="token item">la:</span><span>  </span>language</a></li> <li><a href="#"><span class="token item">pu:</span><span>  </span>publisher</a></li> <li><a href="#"><span class="token item">py:</span><span>  </span>year</a></li> <li><a href="#"><span class="token item">rv:</span><span>  </span>reviewer name</a></li> <li><a href="#"><span class="token item">so:</span><span>  </span>source</a></li> <li><a href="#"><span class="token item">sw:</span><span>  </span>software name</a></li> <li><a href="#"><span class="token item">ti:</span><span>  </span>title</a></li> <li><a href="#"><span class="token item">ut:</span><span>  </span>keyword</a></li> </ul> </div> <div class="btn-group operators"> <button class="btn btn-default dropdown-toggle" data-toggle="dropdown">Operators <i class="caret"></i></button> <ul id="operators" class="dropdown-menu pull-right"> <li><a href="#"><span class="token item">a & b</span><span>  </span>logical and</a></li> <li><a href="#"><span class="token item">a | b</span><span>  </span>logical or</a></li> <li><a href="#"><span class="token item">!ab</span><span>  </span>logical not</a></li> <li><a href="#"><span class="token item">abc*</span><span>  </span>right wildcard</a></li> <li><a href="#"><span class="token item">ab c</span><span>  </span>phrase</a></li> <li><a href="#"><span class="token item">(ab c)</span><span>  </span>parentheses</a></li> </ul> </div> </div> </div> <div class="special"> <ul class="nav help-button"> <li class="dropdown pull-right"> <a href="#">Help <i class="caret"></i></a> </li> </ul> </div> </span> </div> <div class="help"><h2>Examples</h2> <div id="help-terms" role="table"> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Geometry">Geometry</a></span> <span class="search-explanation" role="cell" role="cell">Search for the term <em>Geometry</em> in <strong>any</strong> field. Queries are <strong>case-independent</strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Funct%2A">Funct*</a></span> <span class="search-explanation" role="cell" role="cell"><strong>Wildcard</strong> queries are specified by <u>*</u> (e.g. <em>functions</em>, <em>functorial</em>, etc.). Otherwise the search is <strong>exact</strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Topological+group">Topological group</a></span> <span class="search-explanation" role="cell" role="cell"><strong>Phrases</strong>(multi - words) should be set in <u></u>straight quotation marks<u></u>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=au%3A+Bourbaki+%26+ti%3A+Algebra">au: Bourbaki & ti: Algebra</a></span> <span class="search-explanation" role="cell" role="cell">Search for <strong><u>au</u>thor</strong> <em>Bourbaki</em> and <strong><u>ti</u>tle</strong> <em>Algebra</em>. The <strong>and -operator &</strong> is default and can be omitted.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Chebyshev+%7C+Tschebyscheff">Chebyshev | Tschebyscheff</a></span> <span class="search-explanation" role="cell" role="cell">The <strong>or</strong>-operator <strong>|</strong> allows to search for <em>Chebyshev</em> or <em>Tschebyscheff</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Quasi%2A+map%2A+py%3A+1989">Quasi* map* py: 1989</a></span> <span class="search-explanation" role="cell" role="cell">The resulting documents have <strong><u>p</u>ublication <u>y</u>ear</strong> <em>1989</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=so%3AEur%2A+J%2A+Mat%2A+Soc%2A+cc%3A14">so:Eur* J* Mat* Soc* cc:14</a></span> <span class="search-explanation" role="cell" role="cell">Search for publications in a particular <strong><u>so</u>urce</strong> with a <strong>Mathematics Subject <u>C</u>lassification <u>c</u>ode</strong> in <em>14</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=%27%27Partial+diff%2A+eq%2A%27%27+%21elliptic">''Partial diff* eq*'' !elliptic</a></span> <span class="search-explanation" role="cell" role="cell">The <strong>not</strong> -operator <strong>!</strong> eliminates all results containing the word <em>elliptic</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=dt%3A+b+%26+au%3A+Hilbert">dt: b & au: Hilbert</a></span> <span class="search-explanation" role="cell" role="cell">The <strong><u>d</u>ocument <u>t</u>ype</strong> is set to <u>b</u>ooks; alternatively: <u>j</u> for <strong><u>j</u>ournal articles</strong>, <u>a</u> for <strong>book <u>a</u>rticles</strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=py%3A+2000+-+2015+cc%3A%2894A+%7C+11T%29">py: 2000 - 2015 cc:(94A | 11T)</a></span> <span class="search-explanation" role="cell" role="cell">Number <strong>ranges</strong> when searching for <strong><u>p</u>ublication <u>y</u>ear</strong> are accepted. Terms can be grouped within <strong><u>(</u>parentheses<u>)</u></strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=la%3A+chinese">la: chinese</a></span> <span class="search-explanation" role="cell" role="cell">Find documents in a given <strong><u>la</u>nguage</strong>. <a href='https://en.wikipedia.org/wiki/ISO_639-1'>ISO 639 - 1</a> (opens in new tab) language codes can also be used.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=st%3A+c+r+s">st: c r s</a></span> <span class="search-explanation" role="cell" role="cell">Find documents that are <strong><u>c</u>ited</strong>, have <strong><u>r</u>eferences</strong> and are from a <strong><u>s</u>ingle author</strong>.</span> </div> </div> <p style="margin-bottom:0.5cm;"></p> <h2>Fields</h2> <div id="help-fields" role="table"> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>ab</strong> </span> <span class="search-explanation" role="cell" role="cell"> Text from the summary or review (for phrases use “...”) </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>an</strong> </span> <span class="search-explanation" role="cell" role="cell"> zbMATH ID, i.e.: preliminary ID, Zbl number, JFM number, ERAM number </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>any</strong> </span> <span class="search-explanation" role="cell" role="cell"> Includes ab, au, cc, en, rv, so, ti, ut </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>arxiv</strong> </span> <span class="search-explanation" role="cell" role="cell"> arXiv preprint number </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>au</strong> </span> <span class="search-explanation" role="cell" role="cell"> Name(s) of the contributor(s) </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>br</strong> </span> <span class="search-explanation" role="cell" role="cell"> Name of a person with biographic references (to find documents about the life or work) </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>cc</strong> </span> <span class="search-explanation" role="cell" role="cell"> Code from the Mathematics Subject Classification (prefix with <strong>*</strong> to search only primary MSC) </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>ci</strong> </span> <span class="search-explanation" role="cell" role="cell"> zbMATH ID of a document cited in summary or review </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>db</strong> </span> <span class="search-explanation" role="cell" role="cell"> Database: documents in Zentralblatt für Mathematik/zbMATH Open (<em>db:Zbl</em>), Jahrbuch über die Fortschritte der Mathematik (<em>db:JFM</em>), Crelle's Journal (<em>db:eram</em>), arXiv (<em>db:arxiv</em>) </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>dt</strong> </span> <span class="search-explanation" role="cell" role="cell"> Type of the document: journal article (<em>dt:j</em>), collection article (<em>dt:a</em>), book (<em>dt:b</em>) </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>doi</strong> </span> <span class="search-explanation" role="cell" role="cell"> Digital Object Identifier (DOI) </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>ed</strong> </span> <span class="search-explanation" role="cell" role="cell"> Name of the editor of a book or special issue </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>en</strong> </span> <span class="search-explanation" role="cell" role="cell"> External document ID: DOI, arXiv ID, ISBN, and others </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>in</strong> </span> <span class="search-explanation" role="cell" role="cell"> zbMATH ID of the corresponding issue </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>la</strong> </span> <span class="search-explanation" role="cell" role="cell"> Language (use name, e.g., <em>la:French</em>, or <a href='https://en.wikipedia.org/wiki/ISO_639-1'>ISO 639-1</a>, e.g., <em>la:FR)</em> </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>li</strong> </span> <span class="search-explanation" role="cell" role="cell"> External link (URL) </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>na</strong> </span> <span class="search-explanation" role="cell" role="cell"> Number of authors of the document in question. Interval search with “-” </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>pt</strong> </span> <span class="search-explanation" role="cell" role="cell"> Reviewing state: Reviewed (<em>pt:r</em>), Title Only (<em>pt:t</em>), Pending (<em>pt:p</em>), Scanned Review (<em>pt:s</em>) </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>pu</strong> </span> <span class="search-explanation" role="cell" role="cell"> Name of the publisher </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>py</strong> </span> <span class="search-explanation" role="cell" role="cell"> Year of publication. Interval search with “-” </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>rft</strong> </span> <span class="search-explanation" role="cell" role="cell"> Text from the references of a document (for phrases use “...”) </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>rn</strong> </span> <span class="search-explanation" role="cell" role="cell"> Reviewer ID </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>rv</strong> </span> <span class="search-explanation" role="cell" role="cell"> Name or ID of the reviewer </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>se</strong> </span> <span class="search-explanation" role="cell" role="cell"> Serial ID </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>si</strong> </span> <span class="search-explanation" role="cell" role="cell"> swMATH ID of software referred to in a document </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>so</strong> </span> <span class="search-explanation" role="cell" role="cell"> Bibliographical source, e.g., serial title, volume/issue number, page range, year of publication, ISBN, etc. </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>st</strong> </span> <span class="search-explanation" role="cell" role="cell"> State: is cited (<em>st:c</em>), has references (<em>st:r</em>), has single author (<em>st:s</em>) </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>sw</strong> </span> <span class="search-explanation" role="cell" role="cell"> Name of software referred to in a document </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>ti</strong> </span> <span class="search-explanation" role="cell" role="cell"> Title of the document </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>ut</strong> </span> <span class="search-explanation" role="cell" role="cell"> Keywords </span> </div> </div> <p style="margin-bottom:0.5cm;"></p> <h2>Operators</h2> <div id="operators-fields" role="table"> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"><strong>a & b</strong></span> <span class="search-explanation" role="cell" role="cell">logical and</span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"><strong>a | b</strong></span> <span class="search-explanation" role="cell" role="cell">logical or</span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"><strong>!ab</strong></span> <span class="search-explanation" role="cell" role="cell">logical not</span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"><strong>abc*</strong></span> <span class="search-explanation" role="cell" role="cell">right wildcard</span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"><strong>ab c</strong></span> <span class="search-explanation" role="cell" role="cell">phrase</span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"><strong>(ab c)</strong></span> <span class="search-explanation" role="cell" role="cell">parentheses</span> </div> </div> <p> See also our <a href="/general-help/">General Help</a>. </p></div> </div> </form> <div class="clearfix"></div> </div> <div class="content-shadow"></div> </div> </div> <div id="body"> <div id="main"> <div class="messages"> </div> <div id="documents"> <div class="content-main"> <div class="content-item"><div class="item"> <article> <div class="author"><a href="/authors/ehme.jeffrey-a" title="Author Profile">Ehme, Jeffrey</a>; <a href="/authors/lanz.aprillya" title="Author Profile">Lanz, Aprillya</a></div> <h2 class="title"> <strong>Uniqueness implies existence of solutions for nonlinear focal-like boundary value problems.</strong> <i>(English)</i> <a class="label nowrap" href="/1173.34308">Zbl 1173.34308</a> </h2> <div class="source"> <a href="/serials/1204" title="Journal Profile">Appl. Math. Lett.</a> <a href="/?q=in%3A251154" title="Articles in this Issue">22, No. 9, 1325-1329 (2009)</a>. </div> <div class="abstract"><div class="pre">Summary: Given an appropriate growth condition for $f$ and a uniqueness assumption on $y^{(n)}=0$ with respect to certain focal boundary value problems, it is shown that uniqueness of solutions to the nonlinear differential equation \[ y^{(n)}=f(t,y,y^{\prime},\dots ,y^{(n - 1)}), \] subject to boundary conditions of the form \[ g_{ij}(y(t_j),\dots ,y^{(n - 1)}(t_j))=y_{ij} \] implies existence of solutions.</div></div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A5626185">Cited in <strong>1</strong> Document</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A34B15" title="MSC2020">34B15</a> </td> <td class="space"> Nonlinear boundary value problems for ordinary differential equations </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Auniqueness">uniqueness</a>; <a href="/?q=ut%3Aexistence">existence</a>; <a href="/?q=ut%3Anonlinear+boundary+conditions">nonlinear boundary conditions</a>; <a href="/?q=ut%3Afocal">focal</a>; <a href="/?q=ut%3Aright+focal">right focal</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1173.34308" data-ciurl="/ci/05626185" data-biburl="/bibtex/05626185.bib" data-amsurl="/amsrefs/05626185.bib" data-xmlurl="/xml/05626185.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/05626185.pdf" title="Zbl 1173.34308 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1016/j.aml.2009.03.004" aria-label="DOI for “Uniqueness implies existence of solutions for nonlinear focal-like boundary value problems”" title="10.1016/j.aml.2009.03.004">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Chyan, C.; Henderson, J., Uniqueness implies existence for $(n, p)$ boundary value problems, Appl. Anal., 73, 3-4, 543-556 (1999) · <a href="/1031.34019" class="nowrap">Zbl 1031.34019</a></td> </tr><tr> <td>[2]</td> <td class="space">Davis, J.; Henderson, J., Uniqueness implies existence for fourth-order Lidstone boundary value problems, Panamer. Math. J., 8, 23-35 (1998) · <a href="/0960.34011" class="nowrap">Zbl 0960.34011</a></td> </tr><tr> <td>[3]</td> <td class="space">Hartman, P., On $n$-parameter families and interpolation problems for nonlinear ordinary differential equations, Trans. Am. Math. Soc., 154, 201-226 (1971) · <a href="/0222.34017" class="nowrap">Zbl 0222.34017</a></td> </tr><tr> <td>[4]</td> <td class="space">Henderson, J., Uniqueness of solutions of right focal point boundary value problems for ordinary differential equations, J. Differential Equations, 41, 218-227 (1981) · <a href="/0438.34015" class="nowrap">Zbl 0438.34015</a></td> </tr><tr> <td>[5]</td> <td class="space">Jackson, L., Uniqueness of solutions of boundary value problems for ordinary differential equations, SIAM J. Appl. Math., 24, 4, 535-538 (1973) · <a href="/0237.34030" class="nowrap">Zbl 0237.34030</a></td> </tr><tr> <td>[6]</td> <td class="space">Jackson, L.; Klaasen, G., Uniqueness of solutions of boundary value problems for ordinary differential equations, SIAM J. Appl. Math., 19, 3, 542-546 (1970) · <a href="/0211.11501" class="nowrap">Zbl 0211.11501</a></td> </tr><tr> <td>[7]</td> <td class="space">Peterson, A., Existence-uniqueness for ordinary differential equations, J. Math. Anal. Appl., 64, 166-172 (1978) · <a href="/0386.34022" class="nowrap">Zbl 0386.34022</a></td> </tr><tr> <td>[8]</td> <td class="space">Peterson, A., Existence-uniqueness for focal-point boundary value problems, SIAM J. Math. Anal., 12, 173-185 (1981) · <a href="/0473.34009" class="nowrap">Zbl 0473.34009</a></td> </tr><tr> <td>[9]</td> <td class="space">Henderson, Johnny, Uniqueness implies existence for three-point boundary value problems for second order differential equations, Appl. Math. Lett., 18, 8, 905-909 (2005), 34B10 · <a href="/1092.34507" class="nowrap">Zbl 1092.34507</a></td> </tr><tr> <td>[10]</td> <td class="space">Eloe, Paul W.; Henderson, Johnny, Uniqueness implies existence and uniqueness conditions for nonlocal boundary value problems for $n$ th order differential equations, J. Math. Anal. Appl., 331, 1, 240-247 (2007) · <a href="/1396.34011" class="nowrap">Zbl 1396.34011</a></td> </tr><tr> <td>[11]</td> <td class="space">Abadi; Thompson, H. B., Existence for nonlinear boundary value problems, Comm. Appl. Nonlinear Anal., 5, 4, 41-52 (1998) · <a href="/1110.34303" class="nowrap">Zbl 1110.34303</a></td> </tr><tr> <td>[12]</td> <td class="space">Thompson, H. B., Second order ordinary differential equations with fully nonlinear two point boundary conditions, Pacific J. Math., 172, 1, 255-276 (1996) · <a href="/0855.34024" class="nowrap">Zbl 0855.34024</a></td> </tr><tr> <td>[13]</td> <td class="space">Thompson, H. B., Second order ordinary differential equations with fully nonlinear two point boundary conditions II, Pacific J. Math., 172, 1, 279-297 (1996) · <a href="/0862.34015" class="nowrap">Zbl 0862.34015</a></td> </tr><tr> <td>[14]</td> <td class="space">Thompson, H. B., Systems of differential equations with fully nonlinear boundary conditions, Bull. Austral. Math. Soc., 56, 2, 197-208 (1997) · <a href="/0893.34011" class="nowrap">Zbl 0893.34011</a></td> </tr><tr> <td>[15]</td> <td class="space">Schrader, K., Uniqueness implies existence for solutions of nonlinear boundary value problems, Abstracts Amer. Math. Soc., 6, 235 (1985)</td> </tr><tr> <td>[16]</td> <td class="space">Ehme, J.; Eloe, P. W.; Henderson, J., Existence of solutions for $2 n$ th order nonlinear generalized Sturm-Liouville boundary value problems, Math. Inequal. & Appl., 4, 247-255 (2001) · <a href="/0994.34007" class="nowrap">Zbl 0994.34007</a></td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching. </div> </div></article> </div></div> </div> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="copyright"> © 2025 <a target="fiz" href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe GmbH</a> <a href="/privacy-policy/">Privacy Policy</a> <a href="/legal-notices/">Legal Notices</a> <a href="/terms-conditions/">Terms & Conditions</a> <div class="info"> <ul class="nav"> <li class="mastodon"> <a href="https://mathstodon.xyz/@zbMATH" target="_blank" class="no-new-tab-icon"> <img src="/static/mastodon.png" title="zbMATH at Mathstodon (opens in new tab)" alt="Mastodon logo"> </a> </li> </ul> </div> </div> <div class="clearfix" style="height: 0px;"></div> </div> </div> <script src="https://static.zbmath.org/contrib/jquery/1.9.1/jquery.min.js"></script> <script src="https://static.zbmath.org/contrib/jquery-caret/1.5.2/jquery.caret.min.js"></script> <script src="/static/js/jquery-ui-1.10.1.custom.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap/v3.3.7zb1/js/bootstrap.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.js"></script> <script src="https://static.zbmath.org/contrib/retina/unknown/retina.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/js/bootstrap-select.min.js"></script> <script> var SCRIPT_ROOT = ""; </script> <script src="/static/scripts.js?v=20250307"></script> <script src="https://static.zbmath.org/contrib/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ "HTML-CSS": { preferredFont: "TeX", availableFonts: [ "STIX", "TeX" ], linebreaks: { automatic: true }, EqnChunk: (MathJax.Hub.Browser.isMobile ? 10 : 50) }, tex2jax: { processEscapes: true, ignoreClass: "tex2jax_ignore|dno" }, TeX: { Macros: { Aut: "\\operatorname{Aut}", Hom: "\\operatorname{Hom}" }, noUndefined: { attributes: { mathcolor: "#039", //"red", mathbackground: "white", //"#FFEEEE", mathsize: "90%" } } }, messageStyle: "none" }); </script> <script type="text/javascript"> $(document).ready(function() { $("#MathInput").stop(true, true).keyup(function() { $.ajax({ url: "/mwsq/", type: "POST", data: { query : $("#MathInput").val() }, dataType: "text" }) .done(function(xml) { $("#MathPreview").html(xml); $(window).resize(); }); }); var press = jQuery.Event("keyup"); press.ctrlKey = false; press.which = 40; $("#MathInput").trigger(press); }); </script> <div id="new_tab_icon" style="display: none"> <span class="glyphicon glyphicon-new-window" aria-hidden="true"></span><span class="sr-only">(opens in new tab)</span></div> </body> </html>

CINXE.COM

Document Zbl 1173.34308 - zbMATH Open