This paper deals with existence and multiplicity of solutions to the nonlinear Schrodinger equation of the type -Deltau+(lambdaa(x) + a(o)(x))u = f(x, u), u is an element of H-1 (R-N). We improve some previous results in two respects: we do not require a(o) to be positive on one hand, and allow f(x,u) to be critical nonlinear on the other hand.83563584