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

Abstract

We are concerned with a system of coupled Schrödinger equations $$-\Delta u_i+V_i(x)u_i={\partial }_{u_i}F(x,u)on{\mathbb{R}}^N,i=1,2,...,K,$$ where $F$ and $V_i$ are periodic in $x$ and $0\notin \sigma (-\Delta +V_i)$ for $i=1,2,...,K$, where $\sigma (-\Delta +V_i)$ stands for the spectrum of the Schrödinger 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.

to appear in Comm. Partial Differential Equations

References in corpus (1)

• Ground and bound state solutions of semilinear time-harmonic Maxwell equations in a bounded domain

Cited by in corpus (6)

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• The fractional Schrödinger equation with Hardy-type potentials and sign-changing nonlinearities
• Systems of coupled Schrödinger equations with sign-changing nonlinearities via classical Nehari manifold approach
• Generalized linking-type theorem with applications to strongly indefinite problems with sign-changing nonlinearities
• Note on semiclassical states for the Schrödinger equation with nonautonomous nonlinearities