Document Zbl 1459.35223

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Anal.</a> <a href="/?q=in%3A458206" title="Articles in this Issue">99, No. 9, 1631-1637 (2020)</a>. </div> <div class="abstract">Summary: The existence and uniqueness of positive radial solutions are obtained for a mean curvature equation in Lorentz-Minkowski space of the form \[\begin{aligned} & \operatorname{div} \left(\frac{\nabla v}{\sqrt{1- |\nabla v|^2}}\right) + f(|x|, v) = 0 \quad \text{in }\Omega, \\ & v = 0 \quad \text{on } \partial\Omega, \end{aligned}\] where $\Omega$ is a unit ball in $\mathbb{R}^N, f(r,u)$ may be singular at $r=0$ and/or $r=1$, and strongly singular at $u=0$. The main tool is the perturbation technique and Schauder fixed point theorem.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7304794">Cited in <strong>2</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A35J93" title="MSC2020">35J93</a> </td> <td class="space"> Quasilinear elliptic equations with mean curvature operator </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35J75" title="MSC2020">35J75</a> </td> <td class="space"> Singular elliptic equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35A01" title="MSC2020">35A01</a> </td> <td class="space"> Existence problems for PDEs: global existence, local existence, non-existence </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35A02" title="MSC2020">35A02</a> </td> <td class="space"> Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Amean+curvature+equation">mean curvature equation</a>; <a href="/?q=ut%3Astrong+singularity">strong singularity</a>; <a href="/?q=ut%3Aexistence+and+uniqueness+of+positive+radial+solutions">existence and uniqueness of positive radial solutions</a>; <a href="/?q=ut%3ASchauder+fixed+point+theorem">Schauder fixed point theorem</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 1459.35223" data-ciurl="/ci/07304794" data-biburl="/bibtex/07304794.bib" data-amsurl="/amsrefs/07304794.bib" data-xmlurl="/xml/07304794.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07304794.pdf" title="Zbl 1459.35223 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/10.1080/00036811.2018.1555322" aria-label="DOI for “Positive radial solutions of a mean curvature equation in Lorentz-Minkowski space with strong singularity”" title="10.1080/00036811.2018.1555322">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">Albujer, AL; 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Wang, L., Multiplicity of positive radial solutions of a singular mean curvature equations in Minkowski space, Appl Math Lett, 60, 50-55 (2016) · <a href="/1341.35079" class="nowrap">Zbl 1341.35079</a> · <a href="https://doi.org/10.1016/j.aml.2016.04.001" class="nowrap">doi:10.1016/j.aml.2016.04.001</a></td> </tr><tr> <td>[14]</td> <td class="space">Pei, M.; Wang, L., Positive radial solutions of a mean curvature equations in Minkowski space with strong singularity, Proc Am Math Soc, 145, 4423-4430 (2017) · <a href="/1375.35231" class="nowrap">Zbl 1375.35231</a> · <a href="https://doi.org/10.1090/proc/13587" class="nowrap">doi:10.1090/proc/13587</a></td> </tr><tr> <td>[15]</td> <td class="space">Rudin, W., Real and complex analysis (1986), New York: McGraw-Hill Book Company, New York</td> </tr><tr> <td>[16]</td> <td class="space">Ma, X.; Xu, J., Gradient estimates of mean curvature equations with Neumann boundary condition, Adv Math, 290, 1010-1039 (2014) · <a href="/1335.35084" class="nowrap">Zbl 1335.35084</a> · <a href="https://doi.org/10.1016/j.aim.2015.10.031" class="nowrap">doi:10.1016/j.aim.2015.10.031</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=20240926"> </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>

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