Infinitely many solutions for nonlinear Schrödinger systems with magnetic potentials in R 3

We study the following nonlinear Schrödinger system with magnetic potentials inR 3 :∇ i − A ( y )2 u + P ( y ) u = μ 1 | u | 2 u + β | v | 2 u ,y ∈ R 3 ,∇ i − A ( y )2 v + Q ( y ) v = μ 2 | v | 2 v + β | u | 2 v ,y ∈ R 3 ,where μ 1 >0, μ 2 >0, and β ∈ R is a coupling constant. Under some weak symmetry conditions on A ( y ), P ( y ), and Q ( y ), which are given in the introduction, we prove that the nonlinear Schrödinger system has infinitely many non‐radial complex‐valued segregated and synchronized solutions. Copyright © 2015 John Wiley & Sons, Ltd.