A global compactness result for singular elliptic problems involving critical Sobolev exponent

Let $\Omega \subset R^N$ be a bounded domain such that $0 \in \Omega, N \geq 3,2^*=\frac{2N}{N-2},\lambda \in R, \epsilon \in R$. Let $\{u_n\}\subset H_0^1(\Omega)$ be a (P.S.) sequence of the functional $E_{\lambda,\epsilon}(u)=\frac{1}{2}\int_{\Omega}(\vert\nabla u\vert^{2}-\frac{\... ...^2}{\vert x\vert^2}-\epsilon u^2)-\frac{1}{2^*}\int_{\Omega} \vert u\vert^{2^*}$. We study the limit behaviour of $u_n$ and obtain a global compactness result.