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Infinitely many solutions for nonlinear Schrödinger systems with magnetic potentials in R 3
Author(s) -
Liu Weiming
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3581
Subject(s) - nonlinear system , mathematics , schrödinger's cat , coupling constant , symmetry (geometry) , constant (computer programming) , mathematical physics , coupling (piping) , schrödinger equation , mathematical analysis , physics , quantum mechanics , geometry , computer science , engineering , mechanical engineering , programming language
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.