{"title":"加权索波列夫空间上的非线性椭圆方程","authors":"Rupali Kumari, Rasmita Kar","doi":"10.1134/s0001434623110603","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> The main objective of this work is to show the existence of solutions for quasilinear elliptic boundary value problem. In addition, we study compactness, directness of the solution set along with existence of smallest and biggest solutions in the set. The presence of dependence on the gradient and the Leray–Lions operator are the main novelties. We have used sub-supersolution technique in our work. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Nonlinear Elliptic Equations on Weighted Sobolev Space\",\"authors\":\"Rupali Kumari, Rasmita Kar\",\"doi\":\"10.1134/s0001434623110603\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3 data-test=\\\"abstract-sub-heading\\\">Abstract</h3><p> The main objective of this work is to show the existence of solutions for quasilinear elliptic boundary value problem. In addition, we study compactness, directness of the solution set along with existence of smallest and biggest solutions in the set. The presence of dependence on the gradient and the Leray–Lions operator are the main novelties. We have used sub-supersolution technique in our work. </p>\",\"PeriodicalId\":18294,\"journal\":{\"name\":\"Mathematical Notes\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-03-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Notes\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1134/s0001434623110603\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Notes","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0001434623110603","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Nonlinear Elliptic Equations on Weighted Sobolev Space
Abstract
The main objective of this work is to show the existence of solutions for quasilinear elliptic boundary value problem. In addition, we study compactness, directness of the solution set along with existence of smallest and biggest solutions in the set. The presence of dependence on the gradient and the Leray–Lions operator are the main novelties. We have used sub-supersolution technique in our work.
期刊介绍:
Mathematical Notes is a journal that publishes research papers and review articles in modern algebra, geometry and number theory, functional analysis, logic, set and measure theory, topology, probability and stochastics, differential and noncommutative geometry, operator and group theory, asymptotic and approximation methods, mathematical finance, linear and nonlinear equations, ergodic and spectral theory, operator algebras, and other related theoretical fields. It also presents rigorous results in mathematical physics.