k-convex solutions for multiparameter Dirichlet systems with k-Hessian operator and Lane-Emden type nonlinearities

IF 4.3 3区材料科学 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC

ACS Applied Electronic Materials Pub Date : 2024-01-01 DOI:10.1515/anona-2023-0136

Xingyue He, Chenghua Gao, Jingjing Wang

{"title":"k-convex solutions for multiparameter Dirichlet systems with k-Hessian operator and Lane-Emden type nonlinearities","authors":"Xingyue He, Chenghua Gao, Jingjing Wang","doi":"10.1515/anona-2023-0136","DOIUrl":null,"url":null,"abstract":"\n In this article, our main aim is to investigate the existence of radial \n \n \n <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\n <m:mi>k</m:mi>\n </m:math>\n k\n \n -convex solutions for the following Dirichlet system with \n \n \n <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\n <m:mi>k</m:mi>\n </m:math>\n k\n \n -Hessian operators: \n \n \n <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" display=\"block\">\n <m:mfenced open=\"{\" close=\"\">\n <m:mrow>\n <m:mtable displaystyle=\"true\">\n <m:mtr>\n <m:mtd columnalign=\"left\">\n <m:msub>\n <m:mrow>\n <m:mi>S</m:mi>\n </m:mrow>\n <m:mrow>\n <m:mi>k</m:mi>\n </m:mrow>\n </m:msub>\n <m:mrow>\n <m:mo>(</m:mo>\n <m:mrow>\n <m:msup>\n <m:mrow>\n <m:mi>D</m:mi>\n </m:mrow>\n <m:mrow>\n <m:mn>2</m:mn>\n </m:mrow>\n </m:msup>\n <m:mi>u</m:mi>\n </m:mrow>\n <m:mo>)</m:mo>\n </m:mrow>\n <m:mo>=</m:mo>\n <m:msub>\n <m:mrow>\n <m:mi>λ</m:mi>\n </m:mrow>\n <m:mrow>\n <m:mn>1</m:mn>\n </m:mrow>\n </m:msub>\n <m:msub>\n <m:mrow>\n <m:mi>ν</m:mi>\n </m:mrow>\n <m:mrow>\n <m:mn>1</m:mn>\n </m:mrow>\n </m:msub>\n <m:mrow>\n <m:mo>(</m:mo>\n <m:mrow>\n <m:mo>∣</m:mo>\n <m:mi>x</m:mi>\n <m:mo>∣</m:mo>\n </m:mrow>\n <m:mo>)</m:mo>\n </m:mrow>\n <m:msup>\n <m:mrow>\n <m:mrow>\n <m:mo>(</m:mo>\n <m:mrow>\n <m:mo>−</m:mo>\n <m:mi>u</m:mi>\n </m:mrow>\n <m:mo>)</m:mo>\n </m:mrow>\n </m:mrow>\n <m:mrow>\n <m:msub>\n <m:mrow>\n <m:mi>p</m:mi>\n </m:mrow>\n <m:mrow>\n <m:mn>1</m:mn>\n </m:mrow>\n </m:msub>\n </m:mrow>\n </m:msup>\n <m:msup>\n <m:mrow>\n <m:mrow>\n <m:mo>(</m:mo>\n <m:mrow>\n <m:mo>−</m:mo>\n <m:mi>v</m:mi>\n </m:mrow>\n <m:mo>)</m:mo>\n </m:mrow>\n </m:mrow>\n <m:mrow>\n <m:msub>\n <m:mrow>\n <m:mi>q</m:mi>\n </m:mrow>\n <m:mrow>\n <m:mn>1</m:mn>\n </m:mrow>\n </m:msub>\n </m:mrow>\n </m:msup>\n </m:mtd>\n <m:mtd columnalign=\"left\">\n <m:mi mathvariant=\"normal\">in</m:mi>\n <m:mspace width=\"1em\" />\n <m:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">ℬ</m:mi>\n <m:mrow>\n <m:mo>(</m:mo>\n <m:mrow>\n <m:mi>R</m:mi>\n </m:mrow>\n <m:mo>)</m:mo>\n </m:mrow>\n <m:mo>,</m:mo>\n </m:mtd>\n </m:mtr>\n <m:mtr>\n <m:mtd columnalign=\"left\">\n <m:msub>\n <m:mrow>\n <m:mi>S</m:mi>\n </m:mrow>\n <m:mrow>\n <m:mi>k</m:mi>\n </m:mrow>\n </m:msub>\n <m:mrow>\n <m:mo>(</m:mo>\n <m:mrow>\n <m:msup>\n <m:mrow>\n <m:mi>D</m:mi>\n </m:mrow>\n <m:mrow>\n <m:mn>2</m:mn>\n </m:mrow>\n </m:msup>\n <m:mi>v</m:mi>\n </m:mrow>\n <m:mo>)</m:mo>\n </m:mrow>\n <m:mo>=</m:mo>\n <m:msub>\n <m:mrow>\n <m:mi>λ</m:mi>\n </m:mrow>\n <m:mrow>\n <m:mn>2</m:mn>\n ","PeriodicalId":3,"journal":{"name":"ACS Applied Electronic Materials","volume":null,"pages":null},"PeriodicalIF":4.3000,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Electronic Materials","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/anona-2023-0136","RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}