A borderline case in elliptic problems involving weights of Caffarelli–Kohn–Nirenberg type

This work deals with problems {−div(|x|−2γ∇u)−(N−2(γ+1)2)2u|x|2(γ+1)=fλ(x,u),u>0in Ω,u=0on ∂Ω, with different kinds of nonlinear functions fλ(x,u)fλ(x,u), that will be specified in each statement. The main difficulties come from the presence of the constant (N−2(γ+1)2)2 which is the optimal one in the Hardy–Sobolev inequalities. This leads to a nontrivial adaptation of the functional framework.