Ground state solutions for a periodic Schrödinger equation with superlinear nonlinearities

In this paper we consider the following Schrödinger equation: {−Δu+V(x)u=g(x,u)forx∈RN,u(x)→0as|x|→∞ where VV is a periodic continuous real function with 0 in a gap of the spectrum σ(A),A≔−Δ+Vσ(A),A≔−Δ+V and the classical Ambrosetti–Rabinowitz superlinear condition on gg is replaced by a general super-quadratic condition.