{"title":"Multiple Solutions of a Nonlocal Problem with Nonlinear Boundary Conditions","authors":"Jie Liu, Qing Miao","doi":"10.1155/2024/3621001","DOIUrl":null,"url":null,"abstract":"In this article, we consider a class of nonlocal <i>p</i>(<i>x</i>)-Laplace equations with nonlinear boundary conditions. When the nonlinear boundary involves critical exponents, using the concentration compactness principle, mountain pass lemma, and fountain theorem, we can prove the existence and multiplicity of solutions.","PeriodicalId":55177,"journal":{"name":"Discrete Dynamics in Nature and Society","volume":"55 1","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2024-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Dynamics in Nature and Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1155/2024/3621001","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
In this article, we consider a class of nonlocal p(x)-Laplace equations with nonlinear boundary conditions. When the nonlinear boundary involves critical exponents, using the concentration compactness principle, mountain pass lemma, and fountain theorem, we can prove the existence and multiplicity of solutions.
期刊介绍：
The main objective of Discrete Dynamics in Nature and Society is to foster links between basic and applied research relating to discrete dynamics of complex systems encountered in the natural and social sciences. The journal intends to stimulate publications directed to the analyses of computer generated solutions and chaotic in particular, correctness of numerical procedures, chaos synchronization and control, discrete optimization methods among other related topics. The journal provides a channel of communication between scientists and practitioners working in the field of complex systems analysis and will stimulate the development and use of discrete dynamical approach.
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