Existence of solutions for elliptic problems with critical Sobolev-Hardy exponents

Let Ω ⊂ ℝN be a smooth bounded domain such that 0 ∈ Ω,N≥3, 0≤s<2,2* (s)=2(N−s)/(N−2). We prove the existence of nontrival solutions for the singular critical problem\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$ - \Delta u - \mu \frac{u}{{\left| x \right|^2 }} = \frac{{\left| u \right|^{2^* \left( s \right) - 2} }}{{\left| x \right|^s }}u + \lambda u$$ \end{document} with Dirichlet boundary condition on Ω for suitable positive parameters λ and μ.