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{"title":"Infinitely many solutions for Hamiltonian system with critical growth","authors":"Yuxia Guo, Yichen Hu","doi":"10.1515/anona-2023-0134","DOIUrl":null,"url":null,"abstract":"\n <jats:p>In this article, we consider the following elliptic system of Hamiltonian-type on a bounded domain:<jats:disp-formula id=\"j_anona-2023-0134_eq_001\">\n <jats:alternatives>\n <jats:graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_anona-2023-0134_eq_001.png\" />\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:mo>−</m:mo>\n <m:mi mathvariant=\"normal\">Δ</m:mi>\n <m:mi>u</m:mi>\n <m:mo>=</m:mo>\n <m:msub>\n <m:mrow>\n <m:mi>K</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>y</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:mo>∣</m:mo>\n <m:mi>v</m:mi>\n <m:mo>∣</m:mo>\n </m:mrow>\n <m:mrow>\n <m:mi>p</m:mi>\n <m:mo>−</m:mo>\n <m:mn>1</m:mn>\n </m:mrow>\n </m:msup>\n <m:mi>v</m:mi>\n <m:mo>,</m:mo>\n <m:mspace width=\"1.0em\" />\n </m:mtd>\n <m:mtd columnalign=\"left\">\n <m:mspace width=\"0.1em\" />\n <m:mtext>in</m:mtext>\n <m:mspace width=\"0.1em\" />\n <m:mspace width=\"0.33em\" />\n <m:msub>\n <m:mrow>\n <m:mi>B</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:mn>0</m:mn>\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:mo>−</m:mo>\n <m:mi mathvariant=\"normal\">Δ</m:mi>\n <m:mi>v</m:mi>\n <m:mo>=</m:mo>\n <m:msub>\n <m:mrow>\n <m:mi>K</m:mi>\n </m:mrow>\n <m:mrow>\n <m:mn>2</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>y</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:mo>∣</m:mo>\n <m:mi>u</m:mi>\n <m:mo>∣</m:mo>\n </m:mrow>\n <m:mrow>\n <m:mi>q</m:mi>\n <m:mo>−</m:mo>\n <m:mn>1</m:mn>\n </m:mrow>\n </m:msup>\n <m:mi>u</m:mi>\n <m:mo>,</m:mo>\n <m:mspace width=\"1.0em\" />\n </m:mtd>\n <m:mtd columnalign=\"left\">\n <m:mspace width=\"0.1em\" />\n <m:mtext>in</m:mtext>\n <m:mspace width=\"0.1em\" />\n <m:mspace width=\"0.33em\" />\n <m:msub>\n <m:mrow>\n <m:mi>B</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:mn>0</m:mn>\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:mi>u</m:mi>\n <m:mo>=</m:mo>\n <m:mi>v</m:mi>\n <m:mo>=</m:mo>\n <m:mn>0</m:mn>\n <m:mspace width=\"1.0em\" />\n </m:mtd>\n <m:mtd columnalign=\"left\">\n <m:mspace width=\"0.1em\" />\n <m:mtext>on</m:mtext>\n <m:mspace width=\"0.1em\" />\n <m:mspace width=\"0.33em\" />\n <m:mo>∂</m:mo>\n <m:msub>\n <m:mrow>\n <m:mi>B</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:mn>0</m:mn>\n </m:mrow>\n <m:mo>)</m:mo>\n </m:mrow>\n <m:mo>,</m:mo>\n </m:mtd>\n </m:mtr>\n </m:mtable>\n </m:mrow>\n </m:mfenced>\n </m:math>\n <jats:tex-math>\\left\\{\\begin{array}{ll}-\\Delta u={K}_{1}\\left(| y| ){| v| }^{p-1}v,\\hspace{1.0em}& \\hspace{0.1em}\\text{in}\\hspace{0.1em}\\hspac","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":3.2000,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Nonlinear Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/anona-2023-0134","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
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具有临界增长的哈密顿系统的无限多解
在本文中,我们考虑以下有界域上的哈密顿型椭圆系统: - Δ u = K 1 ( ∣ y ∣ ) ∣ v ∣ p - 1 v , in B 1 ( 0 ) , - Δ v = K 2 ( ∣ y ∣ ) ∣ u ∣ q - 1 u , in
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