On Elliptic Systems involving critical Hardy-Sobolev exponents (Part II)

2015/04/12 by Xuexiu Zhong, Wenming Zou, Zhong, Xuexiu +1
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1504.02939

openalex publication_date 2015/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is the second part of a work devoted to the study of elliptic systems involving multiple Hardy-Sobolev critical exponents: \begincases -Δu-λ\frac|u|^{2^*(s₁)-2}u|x|^s₁=κα\frac1|x|^s₂|u|^α-2u|v|^β amp;\hboxin Ω,
-Δv-μ\frac|v|^{2^*(s₁)-2}v|x|^s₁=κβ\frac1|x|^s₂|u|^α|v|^β-2v amp;\hboxin Ω,
κgt;0,(u,v)∈ \mathscrD:=D₀^1,2(Ω)× D₀^1,2(Ω), \endcases where s₁≠ s₂∈ (0,2), α>1,β>1, λ>0,μ>0,κ>0, α+β=2^*(s₂). Here, 2^*(s):=(2(N-s))/(N-2) is the critical Hardy-Sobolev exponent. When Ω is a cone (especially Ω=\R₊^N or Ω=\R^N), we study the existence of positive ground state solution.

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