求助PDF
{"title":"Existence of solutions for (p(y),q(y))-Laplacian elliptic problem on an exterior domain","authors":"Akanksha Kesarwani, Rasmita Kar","doi":"10.1515/gmj-2024-2022","DOIUrl":null,"url":null,"abstract":"\n <jats:p>In this paper, we study the following elliptic problem involving the (<jats:inline-formula id=\"j_gmj-2024-2022_ineq_9999\">\n <jats:alternatives>\n <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\n <m:mrow>\n <m:mrow>\n <m:mi>p</m:mi>\n <m:mo></m:mo>\n <m:mrow>\n <m:mo stretchy=\"false\">(</m:mo>\n <m:mi>y</m:mi>\n <m:mo stretchy=\"false\">)</m:mo>\n </m:mrow>\n </m:mrow>\n <m:mo>,</m:mo>\n <m:mrow>\n <m:mi>q</m:mi>\n <m:mo></m:mo>\n <m:mrow>\n <m:mo stretchy=\"false\">(</m:mo>\n <m:mi>y</m:mi>\n <m:mo stretchy=\"false\">)</m:mo>\n </m:mrow>\n </m:mrow>\n </m:mrow>\n </m:math>\n <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2022_eq_0339.png\"/>\n <jats:tex-math>{p(y),q(y)}</jats:tex-math>\n </jats:alternatives>\n </jats:inline-formula>)-Laplacian operator:</jats:p>\n <jats:p>\n <jats:disp-formula id=\"j_gmj-2024-2022_eq_9999\">\n <jats:alternatives>\n <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\n <m:mrow>\n <m:mo>{</m:mo>\n <m:mtable columnspacing=\"0pt\" displaystyle=\"true\" rowspacing=\"0pt\">\n <m:mtr>\n <m:mtd columnalign=\"right\">\n <m:mrow>\n <m:mrow>\n <m:mrow>\n <m:mo>-</m:mo>\n <m:mrow>\n <m:mi>div</m:mi>\n <m:mo></m:mo>\n <m:mrow>\n <m:mo stretchy=\"false\">(</m:mo>\n <m:mrow>\n <m:mi>a</m:mi>\n <m:mo></m:mo>\n <m:mrow>\n <m:mo stretchy=\"false\">(</m:mo>\n <m:mi>y</m:mi>\n <m:mo stretchy=\"false\">)</m:mo>\n </m:mrow>\n <m:mo></m:mo>\n <m:msup>\n <m:mrow>\n <m:mo stretchy=\"false\">|</m:mo>\n <m:mrow>\n <m:mo>∇</m:mo>\n <m:mo></m:mo>\n <m:mi>v</m:mi>\n </m:mrow>\n <m:mo stretchy=\"false\">|</m:mo>\n </m:mrow>\n <m:mrow>\n <m:mrow>\n <m:mi>p</m:mi>\n <m:mo></m:mo>\n <m:mrow>\n <m:mo stretchy=\"false\">(</m:mo>\n <m:mi>y</m:mi>\n <m:mo stretchy=\"false\">)</m:mo>\n </m:mrow>\n </m:mrow>\n <m:mo>-</m:mo>\n <m:mn>2</m:mn>\n </m:mrow>\n </m:msup>\n <m:mo></m:mo>\n <m:mrow>\n <m:mo>∇</m:mo>\n <m:mo></m:mo>\n <m:mi>v</m:mi>\n </m:mrow>\n </m:mrow>\n <m:mo stretchy=\"false\">)</m:mo>\n </m:mrow>\n </m:mrow>\n </m:mrow>\n <m:mo>+</m:mo>\n <m:mrow>\n <m:mi>b</m:mi>\n <m:mo></m:mo>\n <m:mrow>\n <m:mo stretchy=\"false\">(</m:mo>\n <m:mi>y</m:mi>\n <m:mo stretchy=\"false\">)</m:mo>\n </m:mrow>\n <m:mo></m:mo>\n <m:msup>\n <m:mrow>\n <m:mo stretchy=\"false\">|</m:mo>\n <m:mi>v</m:mi>\n <m:mo stretchy=\"false\">|</m:mo>\n </m:mrow>\n <m:mrow>\n <m:mrow>\n <m:mi>p</m:mi>\n <m:mo></m:mo>\n <m:mrow>\n <m:mo stretchy=\"false\">(</m:mo>\n <m:mi>y</m:mi>\n <m:mo stretchy=\"false\">)</m:mo>\n </m:mrow>\n </m:mrow>\n <m:mo>-</m:mo>\n <m:mn>2</m:mn>\n </m:mrow>\n </m:msup>\n <m:mo></m:mo>\n <m:mi>v</m:mi>\n </m:mrow>\n </m:mrow>\n <m:mo>-</m:mo>\n <m:mrow>\n <m:mi>div</m:mi>\n <m:mo></m:mo>\n <m:mrow>\n <m:mo stretchy=\"false\">(</m:mo>\n <m:mrow>\n <m:msup>\n <m:mrow>\n <m:mo stretchy=\"false\">|</m:mo>\n <m:mrow>\n <m:mo>∇</m:mo>\n <m:mo></m:mo>\n <m:mi>v</m:mi>\n </m:mrow>\n <m:mo stretchy=\"false\">|</m:mo>\n </m:mrow>\n <m:mrow>\n <m:mrow>\n <m:mi>q</m:mi>\n <m:mo></m:mo>\n <m:mrow>\n <m:mo stretchy=\"false\">(</m:mo>\n <m:mi>y</m:mi>\n ","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Georgian Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/gmj-2024-2022","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
引用
批量引用
外部域上 (p(y),q(y))-拉普拉斯椭圆问题解的存在性
本文研究了以下涉及 ( p ( y ) , q ( y ) {p(y),q(y)} )- 拉普拉卡算子的椭圆问题: { - div ( a ( y ) | ∇ v | p ( y ) - 2 ∇ v ) + b ( y ) | v
本文章由计算机程序翻译,如有差异,请以英文原文为准。