{"title":"Competing anisotropic and Finsler \\((p,q)\\)-Laplacian problems","authors":"Dumitru Motreanu, Abdolrahman Razani","doi":"10.1186/s13661-024-01847-1","DOIUrl":null,"url":null,"abstract":"The aim of this paper is to prove the existence of generalized variational solutions for nonlinear Dirichlet problems driven by anisotropic and Finsler Laplacian competing operators. The main difficulty consists in the lack of ellipticity and monotonicity in the principal part of the equations. This difficulty is overcome by developing a Galerkin-type procedure.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":null,"pages":null},"PeriodicalIF":1.7000,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Boundary Value Problems","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1186/s13661-024-01847-1","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
Abstract
The aim of this paper is to prove the existence of generalized variational solutions for nonlinear Dirichlet problems driven by anisotropic and Finsler Laplacian competing operators. The main difficulty consists in the lack of ellipticity and monotonicity in the principal part of the equations. This difficulty is overcome by developing a Galerkin-type procedure.
期刊介绍：
The main aim of Boundary Value Problems is to provide a forum to promote, encourage, and bring together various disciplines which use the theory, methods, and applications of boundary value problems. Boundary Value Problems will publish very high quality research articles on boundary value problems for ordinary, functional, difference, elliptic, parabolic, and hyperbolic differential equations. Articles on singular, free, and ill-posed boundary value problems, and other areas of abstract and concrete analysis are welcome. In addition to regular research articles, Boundary Value Problems will publish review articles.
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