Positive solutions to a semilinear elliptic equation with a Sobolev–Hardy term

In this paper, we study the existence of positive solutions to the following semilinear elliptic equation with a Sobolev–Hardy term equation(0.1){−Δu−λu=u2♯−1|y|x∈Ω,u>0,x∈Ω,u∈H01(Ω), where ΩΩ is a bounded domain with smooth boundary in RN(N≥3)RN(N≥3), x=(y,z)∈Ω⊂Rk×RN−k=RNx=(y,z)∈Ω⊂Rk×RN−k=RN, 2≤k