{"title":"具有不连续非线性的p（x）-拉普拉斯算子的Dirichlet边值问题","authors":"M. A. Hammou","doi":"10.24193/mathcluj.2021.2.10","DOIUrl":null,"url":null,"abstract":"In this paper, we prove the existence of a weak solution for the Dirichlet boundary value problem related to a certain p(x)-Laplacian, by using the degree theory after turning the problem into a Hammerstein equation. The right hand side is a possibly discontinuous function in the second variable satisfying some non-standard growth conditions.","PeriodicalId":39356,"journal":{"name":"Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2019-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Dirichlet boundary value problem related to the p(x)-Laplacian with discontinuous nonlinearity\",\"authors\":\"M. A. Hammou\",\"doi\":\"10.24193/mathcluj.2021.2.10\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we prove the existence of a weak solution for the Dirichlet boundary value problem related to a certain p(x)-Laplacian, by using the degree theory after turning the problem into a Hammerstein equation. The right hand side is a possibly discontinuous function in the second variable satisfying some non-standard growth conditions.\",\"PeriodicalId\":39356,\"journal\":{\"name\":\"Mathematica\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-11-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematica\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.24193/mathcluj.2021.2.10\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.24193/mathcluj.2021.2.10","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
Dirichlet boundary value problem related to the p(x)-Laplacian with discontinuous nonlinearity
In this paper, we prove the existence of a weak solution for the Dirichlet boundary value problem related to a certain p(x)-Laplacian, by using the degree theory after turning the problem into a Hammerstein equation. The right hand side is a possibly discontinuous function in the second variable satisfying some non-standard growth conditions.
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