Ground states of a system of nonlinear Schrodinger equations with periodic potentials

摘要

We are concerned with a system of coupled Schrodinger equations where F and V-i are periodic in x and 0 is an element of sigma(-Delta+V-i) for i=1,2,...,K, where sigma(-Delta+V-i) stands for the spectrum of the Schrodinger operator -Delta+V-i. We impose general assumptions on the nonlinearity F with the subcritical growth and we find a ground state solution being a minimizer of the energy functional associated with the system on a Nehari-Pankov manifold. Our approach is based on a new linking-type result involving the Nehari-Pankov manifold.