{"title":"Liouville type theorem and Morse indices of a semilinear elliptic equation with nonlocal nonlinearities","authors":"Xiaowei An, Huixia He, Xianfa Song","doi":"10.1063/5.0091269","DOIUrl":null,"url":null,"abstract":"In this study, we study the solution of a semilinear elliptic equation with nonlocal nonlinearities. By using the mountain pass theorem, Hölder’s inequality, and Sobolev embedding theorem, we obtain the existence result, establish the Liouville type theorem, and consider Morse indices of the equation.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"105 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Physics Analysis Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1063/5.0091269","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this study, we study the solution of a semilinear elliptic equation with nonlocal nonlinearities. By using the mountain pass theorem, Hölder’s inequality, and Sobolev embedding theorem, we obtain the existence result, establish the Liouville type theorem, and consider Morse indices of the equation.
期刊介绍：
Journal of Mathematical Physics, Analysis, Geometry (JMPAG) publishes original papers and reviews on the main subjects:
mathematical problems of modern physics;
complex analysis and its applications;
asymptotic problems of differential equations;
spectral theory including inverse problems and their applications;
geometry in large and differential geometry;
functional analysis, theory of representations, and operator algebras including ergodic theory.
The Journal aims at a broad readership of actively involved in scientific research and/or teaching at all levels scientists.
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