Existence of solutions for singular critical growth semilinear elliptic equations

In this paper, the following semilinear elliptic problem is studied: −Δu−μ u/|x|^2=λu+|u|^{2^⋆−2}u in Ω, with u=0 on ∂Ω, where Ω is an open bounded domain of R^n (n≥3) containing the origin, ∂Ω is the smooth boundary, 2^⋆=2n/(n−2) is the critical Sobolev exponent, 0≤μ<\overline μ=(n−2)2/4 and λ>0. This problem is characterized by the presence of a singularity at the origin and a critical growth term. Its solvability depends on both the space dimension n and the coefficient μ. Existence results for a nontrivial solution are obtained by using variational methods with critical point theory, by constructing minimax levels within a suitable compactness range.