{"title":"论分数奥利兹-索博列夫空间中伪单调算子的拓扑度：非局部椭圆问题的正解研究","authors":"H. El-Houari, H. Sabiki, H. Moussa","doi":"10.1007/s43036-023-00313-6","DOIUrl":null,"url":null,"abstract":"<div><p>In this research, we analyze the existence of infinite sequences of ordered solutions for a class of non-local elliptic problem with Dirichlet boundary condition. The primary techniques employed consist of topological degree theory for mappings of type <span>\\(S_+\\)</span> and minimization arguments in a fractional Orlicz–Sobolev space. Our main results generalize some recent findings in the literature to non-smooth cases.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 2","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On topological degree for pseudomonotone operators in fractional Orlicz-Sobolev spaces: study of positive solutions of non-local elliptic problems\",\"authors\":\"H. El-Houari, H. Sabiki, H. Moussa\",\"doi\":\"10.1007/s43036-023-00313-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this research, we analyze the existence of infinite sequences of ordered solutions for a class of non-local elliptic problem with Dirichlet boundary condition. The primary techniques employed consist of topological degree theory for mappings of type <span>\\\\(S_+\\\\)</span> and minimization arguments in a fractional Orlicz–Sobolev space. Our main results generalize some recent findings in the literature to non-smooth cases.</p></div>\",\"PeriodicalId\":44371,\"journal\":{\"name\":\"Advances in Operator Theory\",\"volume\":\"9 2\",\"pages\":\"\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-01-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Operator Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s43036-023-00313-6\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Operator Theory","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s43036-023-00313-6","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
On topological degree for pseudomonotone operators in fractional Orlicz-Sobolev spaces: study of positive solutions of non-local elliptic problems
In this research, we analyze the existence of infinite sequences of ordered solutions for a class of non-local elliptic problem with Dirichlet boundary condition. The primary techniques employed consist of topological degree theory for mappings of type \(S_+\) and minimization arguments in a fractional Orlicz–Sobolev space. Our main results generalize some recent findings in the literature to non-smooth cases.
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