We consider the existence of bound and ground states for a family of nonlinear elliptic systems in RN , which involves equations with critical power nonlinearities and Hardy- type singular potentials. The equations are coupled by what we call "Schrodinger-Korteweg- de Vries" non-symmetric terms, which arise in some phenomena of fluid mechanics. By means of variational methods, ground states are derived for several ranges of the positive coupling parameter ν. Moreover, by using min-max arguments, we seek bound states under some energy assumptions.
systems of elliptic equations, variational methods, ground states, bound states; compactness principles, critical sobolev, hardy potential, doubly critical problems