Hasnae El Hammar, Mohamed El Ouaarabi, C. Allalou, S. Melliani
{"title":"Variable exponent $p(\\cdot)$-Kirchhoff type problem with convection in variable exponent Sobolev spaces","authors":"Hasnae El Hammar, Mohamed El Ouaarabi, C. Allalou, S. Melliani","doi":"10.5269/bspm.62976","DOIUrl":null,"url":null,"abstract":"We establish the existence of weak solution for a class of $p(x)$-Kirchhoff type problem for the $p(x)$-Laplacian-like operators with Dirichlet boundary condition and with gradient dependence (convection) in the reaction term. Our result is obtained using the topological degree for a class of demicontinuous operators of generalized $(S_{+})$ type and the theory of the variable exponent Sobolev spaces. Our results extend and generalize several corresponding results from the existing literature.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2022-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Boletim Sociedade Paranaense de Matematica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5269/bspm.62976","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
Abstract
We establish the existence of weak solution for a class of $p(x)$-Kirchhoff type problem for the $p(x)$-Laplacian-like operators with Dirichlet boundary condition and with gradient dependence (convection) in the reaction term. Our result is obtained using the topological degree for a class of demicontinuous operators of generalized $(S_{+})$ type and the theory of the variable exponent Sobolev spaces. Our results extend and generalize several corresponding results from the existing literature.