On a class of semilinear Schrödinger equations with indefinite linear part

In this paper, we are concerned with the existence of ground state solutions for Schrödinger equation−Δu+V(x)u=K(x)|u|2⁎−2u+f(x,u),u∈H1(RN), 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.