{"title":"Weak solution of a Neumann boundary value problem with 𝑝(𝑥)-Laplacian-like operator","authors":"Mohamed El Ouaarabi, C. Allalou, S. Melliani","doi":"10.1515/anly-2022-1063","DOIUrl":null,"url":null,"abstract":"Abstract In this paper, we study the existence of a weak solution for a class of Neumann boundary value problems for equations involving the p ( x ) p(x) -Laplacian-like operator. Using a topological degree theory for a class of demicontinuous operators of generalized ( S + ) (S_{+}) -type and the theory of the variable exponent Sobolev spaces, we establish the existence of a weak solution of this problem. Our results extend and generalize several corresponding results from the existing literature.","PeriodicalId":82310,"journal":{"name":"Philosophic research and analysis","volume":"29 1","pages":"271 - 280"},"PeriodicalIF":0.0000,"publicationDate":"2022-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Philosophic research and analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/anly-2022-1063","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 6
Abstract
Abstract In this paper, we study the existence of a weak solution for a class of Neumann boundary value problems for equations involving the p ( x ) p(x) -Laplacian-like operator. Using a topological degree theory for a class of demicontinuous operators of generalized ( S + ) (S_{+}) -type and the theory of the variable exponent Sobolev spaces, we establish the existence of a weak solution of this problem. Our results extend and generalize several corresponding results from the existing literature.