具有临界增长的哈密顿系统的无限多解

IF 3.2 1区数学 Q1 MATHEMATICS

Advances in Nonlinear Analysis Pub Date : 2024-01-01 DOI:10.1515/anona-2023-0134

Yuxia Guo, Yichen Hu

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/>\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\" 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<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 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引用次数: 0

摘要

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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Infinitely many solutions for Hamiltonian system with critical growth

In this article, we consider the following elliptic system of Hamiltonian-type on a bounded domain: − Δ u = K 1 ( ∣ y ∣ ) ∣ v ∣ p − 1 v , in B 1 ( 0 ) , − Δ v = K 2 ( ∣ y ∣ ) ∣ u ∣ q − 1 u , in B 1 ( 0 ) , u = v = 0 on ∂ B 1 ( 0 ) ,

\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

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来源期刊

Advances in Nonlinear Analysis MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

6.00

自引率

9.50%

发文量

审稿时长

30 weeks

期刊介绍： Advances in Nonlinear Analysis (ANONA) aims to publish selected research contributions devoted to nonlinear problems coming from different areas, with particular reference to those introducing new techniques capable of solving a wide range of problems. The Journal focuses on papers that address significant problems in pure and applied nonlinear analysis. ANONA seeks to present the most significant advances in this field to a wide readership, including researchers and graduate students in mathematics, physics, and engineering.