Existence of bound and ground states for an elliptic system with double criticality

We study the existence of bound and ground states for a class nonlinear elliptic systems in RN. These equations involve critical power nonlinearities Hardy-type singular potentials, coupled by term containing up to powers. More precisely, we find if either positive coupling parameter ν is large or small under suitable assumptions on other parameters problem. Furthermore, are found as Mountain-Pass-type points underlying functional constrained Nehari manifold. Our variational approach improves some known results allows us cover ranges which have not been considered previously.