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

Analysis of PDEs