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

@article{Mederski2016GroundSO,
title={Ground states of a system of nonlinear Schr{\"o}dinger equations with periodic potentials},
author={Jaroslaw Mederski},
journal={Communications in Partial Differential Equations},
year={2016},
volume={41},
pages={1426 - 1440}
}

ABSTRACT We are concerned with a system of coupled Schrödinger equations where F and Vi are periodic in x and 0∉σ(−Δ+Vi) for i = 1,2,…,K, where σ(−Δ+Vi) stands for the spectrum of the Schrödinger operator −Δ+Vi. 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… Expand