Ground states of nonlinear Schrödinger equations with potentials

In this paper we study the nonlinear Schrodinger equation: {−Δu+V(x)u=f(x,u),u∈H1(RN). We give general conditions which assure the existence of ground state solutions. Under a Nehari type condition, we show that the standard Ambrosetti–Rabinowitz super-linear condition can be replaced by a more natural super-quadratic condition.