On a perturbed critical semilinear equation with singularity

In this article, we investigate necessary and sufficient conditions on the perturbation ρ for the existence of positive least energy solutions of the critical singular semilinear elliptic equation -Δ u = |u|^2*(s)-2|x|ˢu + ρ(u) with Dirichlet boundary condition in a bounded smooth domain in Rⁿ containing the origin, where 2^*(s)=2(n-s)/n-2 , 0≤ s < 2 < n . We show that the almost necessary and sufficient condition obtained for the case s = 0 in [1] differs conceptually when 0 < s < 2 .