Ground states of nonlinear Schrodinger equations with sum of periodic and inverse-square potentials

We study the existence of solutions of the following nonlinear Schrodinger equation -Delta u + (V(x) - mu/vertical bar x vertical bar(2))u = f (x, u) for x is an element of R-N \ {0}, where V : R-N --> R and f : R-N x R --> R are periodic in x is an element of R-N. We assume that 0 does not lie in the spectrum of -Delta + V and mu < (N-2)(2)/4, N >= 3. The superlinear and subcritical term f satisfies a weak monotonicity condition. For sufficiently small mu >= 0 we find a ground state solution as a minimizer of the energy functional on a natural constraint. If mu < 0 and 0 lies below the spectrum of -Delta + V, then ground state solutions do not exist. (C) 2015 Elsevier Inc. All rights reserved.