On a class of semilinear Schrِdinger equations with indefinite linear part

In this paper, we are concerned with the existence of ground state solutions for Schrödinger equation − Δ u + V ( x ) u = K ( x ) | u | 2 ⁎ − 2 u + f ( x , u ) , u ∈ H 1 ( R N ) , where N ⩾ 4 , V is periodic in x and 0 lies in a spectral gap of − Δ + V , K and f are asymptotically periodic in x.