Ground states for a nonhomogeneous elliptic system involving Hardy–Sobolev critical exponents

Abstract

This paper studies the following nonhomogeneous elliptic system involving Hardy–Sobolev critical exponents {Δu+λ1up−1|x|s+μ1u2*false(s1false)−1|x|s1+αγ2*(s2)uα−1vβ|x|s2=0inΩ,Δv+λ2vp−1|x|s+μ2v2*false(s1false)−1|x|s1+βγ2*(s2)uαvβ−1|x|s2=0inΩ,u≥0,v≥0inΩ,u=0,v=0on∂Ω,where λ1,λ2,μ1,μ2,γ>0,2<p<2*false(sfalse):=2(N−s)N−2,0≤s<2,0<s1,s2<2,α,β>1,α+β=2*false(s2false), Ω is a C1 open bounded domain in RN containing the origin, and N≥4. The existence result of positive ground state solution is established.