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

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: − u+ u = 1+a(x) |u|p−1u +λv, − v + v = 1+b(x) |v|p−1v + λu.