{"title":"Necessary and sufficient condition for existence for a case of eigenvalues of multiplicity two","authors":"Philip Korman","doi":"10.58997/ejde.2024.09","DOIUrl":null,"url":null,"abstract":"We establish necessary and sufficient condition for existence of solutions for a class of semilinear Dirichlet problems with the linear part at resonance at eigenvalues of multiplicity two. The result is applied to give a condition for unboundness of all solutions of the corresponding semilinear heat equation. \nFor more information see https://ejde.math.txstate.edu/Volumes/2024/09/abstr.html","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.58997/ejde.2024.09","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We establish necessary and sufficient condition for existence of solutions for a class of semilinear Dirichlet problems with the linear part at resonance at eigenvalues of multiplicity two. The result is applied to give a condition for unboundness of all solutions of the corresponding semilinear heat equation.
For more information see https://ejde.math.txstate.edu/Volumes/2024/09/abstr.html
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