Existence of symmetric solutions for singular semilinear elliptic systems with critical Hardy–Sobolev exponents

This paper deals with the singular semilinear elliptic system −Δu=μu|x|2+2αQ(x)(α+β)|x|s|u|α−2u|v|β+λ|u|q−2uin Ω,−Δv=μv|x|2+2βQ(x)(α+β)|x|s|u|α|v|β−2v+δ|v|q−2vinΩ,u=v=0on∂Ω, where Ω⊂RN(N≥3)Ω⊂RN(N≥3) is a smooth bounded domain, 0∈Ω0∈Ω and ΩΩ is GG-symmetric with respect to a subgroup GG of O(N)O(N), 0≤μ<μ¯ with μ¯=(N−22)2, λ,δ≥0λ,δ≥0, 0≤s<20≤s<2 and α,β>1α,β>1 satisfy α+β=2∗(s)=2(N−s)N−2, 2