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}
}
  • Jaroslaw Mederski
  • Published 2016
  • Mathematics, Physics
  • Communications in Partial Differential Equations
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
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