Existence of solutions for Hardy-Sobolev-Maz'ya systems

The main goal of this article is to investigate the existence of solutions for the Hardy-Sobolev-Maz'ya system $$displaylines{ -Delta u-lambda frac{u}{|y|^2}=frac{|v|^{p_t-1}}{|y|^t}v,quad hbox{in }Omega,cr -Delta v-lambda frac{v}{|y|^2}=frac{|u|^{p_s-1}}{|y|^s}u,quad hbox{in }Omega,cr u=v=0,quad hbox{on }partial Omega }$$ where $0inOmega$ which is a bounded, open and smooth subset of $mathbb{R}^k imes mathbb{R}^{N-k}$, $2leq k