{"title":"Singular two-phase problem on a complete manifold: analysis and insights","authors":"Omar Benslimane, Ahmed Aberqi","doi":"10.1007/s40065-023-00443-y","DOIUrl":null,"url":null,"abstract":"<div><p>We focus on two-phase problems with singular and superlinear parametric terms on the right-hand side. Using fibering maps and the Nehari manifold method, we prove that there are at least two non-trivial positive solutions in a geometric setting that is locally similar to Euclidean spaces but has different global properties for all except the smallest values of parameter <span>\\(\\mu > 0.\\)</span> Singularities may appear at discrete locations in the manifold, which is a challenge for the work due to the unpredictable behavior of the solution. The findings presented here generalize some known results.</p></div>","PeriodicalId":54135,"journal":{"name":"Arabian Journal of Mathematics","volume":"13 1","pages":"45 - 62"},"PeriodicalIF":0.9000,"publicationDate":"2023-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40065-023-00443-y.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Arabian Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s40065-023-00443-y","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We focus on two-phase problems with singular and superlinear parametric terms on the right-hand side. Using fibering maps and the Nehari manifold method, we prove that there are at least two non-trivial positive solutions in a geometric setting that is locally similar to Euclidean spaces but has different global properties for all except the smallest values of parameter \(\mu > 0.\) Singularities may appear at discrete locations in the manifold, which is a challenge for the work due to the unpredictable behavior of the solution. The findings presented here generalize some known results.
期刊介绍：
The Arabian Journal of Mathematics is a quarterly, peer-reviewed open access journal published under the SpringerOpen brand, covering all mainstream branches of pure and applied mathematics.
Owned by King Fahd University of Petroleum and Minerals, AJM publishes carefully refereed research papers in all main-stream branches of pure and applied mathematics. Survey papers may be submitted for publication by invitation only.To be published in AJM, a paper should be a significant contribution to the mathematics literature, well-written, and of interest to a wide audience. All manuscripts will undergo a strict refereeing process; acceptance for publication is based on two positive reviews from experts in the field.Submission of a manuscript acknowledges that the manuscript is original and is not, in whole or in part, published or submitted for publication elsewhere. A copyright agreement is required before the publication of the paper.Manuscripts must be written in English. It is the author''s responsibility to make sure her/his manuscript is written in clear, unambiguous and grammatically correct language.
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