Existence of solutions for critical elliptic systems with boundary singularities

This article concerns the existence of positive solutions to the nonlinear elliptic system involving critical Hardy-Sobolev exponent $$displaylines{ -Delta u= frac{2lambdaalpha}{alpha+eta} frac{u^{alpha-1} v^eta}{|pi(x)|^s}- u^p, quad hbox{in } Omega,cr -Delta v= frac{2lambdaeta}{alpha+eta} frac{u^alpha v^{eta-1}}{|pi(x)|^s}- v^p, quad hbox{in } Omega,cr u>0,quad v>0, quad hbox{in } Omega,cr u=v=0, quad hbox{on } partialOmega, }$$ where $Ngeq 4$ and $Omega$ is a $C^1$ bounded domain in $mathbb{R}^N$, $01$, $lambda>0$ and $1leq p