{"title":"非线性椭圆型方程Neumann问题的拓扑度方法","authors":"Adil Abbassi, C. Allalou, Abderrazak Kassidi","doi":"10.2478/mjpaa-2020-0018","DOIUrl":null,"url":null,"abstract":"Abstract In this paper, we will use the topological degree, introduced by Berkovits, to prove existence of weak solutions to a Neumann boundary value problems for the following nonlinear elliptic equation -div a(x,u,∇u)=b(x)| u |p-2u+λH(x,u,∇u), - div\\,\\,a\\left( {x,u,\\nabla u} \\right) = b\\left( x \\right){\\left| u \\right|^{p - 2}}u + \\lambda H\\left( {x,u,\\nabla u} \\right), where Ω is a bounded smooth domain of N.","PeriodicalId":36270,"journal":{"name":"Moroccan Journal of Pure and Applied Analysis","volume":"6 1","pages":"231 - 242"},"PeriodicalIF":0.0000,"publicationDate":"2020-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"11","resultStr":"{\"title\":\"Topological degree methods for a Neumann problem governed by nonlinear elliptic equation\",\"authors\":\"Adil Abbassi, C. Allalou, Abderrazak Kassidi\",\"doi\":\"10.2478/mjpaa-2020-0018\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract In this paper, we will use the topological degree, introduced by Berkovits, to prove existence of weak solutions to a Neumann boundary value problems for the following nonlinear elliptic equation -div a(x,u,∇u)=b(x)| u |p-2u+λH(x,u,∇u), - div\\\\,\\\\,a\\\\left( {x,u,\\\\nabla u} \\\\right) = b\\\\left( x \\\\right){\\\\left| u \\\\right|^{p - 2}}u + \\\\lambda H\\\\left( {x,u,\\\\nabla u} \\\\right), where Ω is a bounded smooth domain of N.\",\"PeriodicalId\":36270,\"journal\":{\"name\":\"Moroccan Journal of Pure and Applied Analysis\",\"volume\":\"6 1\",\"pages\":\"231 - 242\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-10-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"11\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Moroccan Journal of Pure and Applied Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2478/mjpaa-2020-0018\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Moroccan Journal of Pure and Applied Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2478/mjpaa-2020-0018","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
Topological degree methods for a Neumann problem governed by nonlinear elliptic equation
Abstract In this paper, we will use the topological degree, introduced by Berkovits, to prove existence of weak solutions to a Neumann boundary value problems for the following nonlinear elliptic equation -div a(x,u,∇u)=b(x)| u |p-2u+λH(x,u,∇u), - div\,\,a\left( {x,u,\nabla u} \right) = b\left( x \right){\left| u \right|^{p - 2}}u + \lambda H\left( {x,u,\nabla u} \right), where Ω is a bounded smooth domain of N.