Existence of positive solutions for the Hénon equation involving critical Sobolev terms

Let N⩾3N⩾3, 2*=2N/(N−2)2*=2N/(N−2) and Ω⊂RNΩ⊂RN be a bounded domain with a smooth boundary ∂Ω   and 0∈Ω0∈Ω. Our purpose in this paper is to consider the existence of solutions of Hénon equation:{−Δu(x)=|x|α|u(x)|2*−1in Ω,u>0in Ω,u=0on ∂Ω, where α>0α>0.