Ground state solution and multiple solutions to asymptotically linear Schrödinger equations

In this paper, we consider the Schrödinger equation −Δu+V(x)u=f(x,u), x∈RN, where V and f are periodic in x1,…,xN, asymptotically linear and satisfies a monotonicity condition. We use the generalized Nehari manifold methods to obtain a ground state solution and infinitely many geometrically distinct solutions when f is odd in u.