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

This work deals with problems View the MathML source{−div(|x|−2γ∇u)−(N−2(γ+1)2)2u|x|2(γ+1)=fλ(x,u),u>0in Ω,u=0on ∂Ω, Turn MathJax on 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 View the MathML source(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.