Solitons of linearly coupled systems of semilinear non-autonomous equations on RnRn

Using concentration compactness type arguments, we prove some results about the existence of positive ground and bound state of the following system of nonlinear Schrödinger equations:{−Δu+u=(1+a(x))|u|p−1u+λv,−Δv+v=(1+b(x))|v|p−1v+λu.