Multiple sign-changing and semi-nodal solutions for coupled Schrödinger equations
Journal
Journal of Differential Equations
Journal Volume
255
Journal Issue
11
Pages
4289-4311
Date Issued
2013
Author(s)
Abstract
We study the following coupled Schrödinger equations which have appeared as several models from mathematical physics:{-δu1+λ1u1=μ1u13+βu1u22,x∈Ω,-δu2+λ2u2=μ2u23+βu12u2,x∈Ω,u1=u2=0on ∂Ω. Here Ω⊂RN (N=2, 3) is a smooth bounded domain, λ1, λ2, μ1, μ2 are all positive constants. We show that, for each k∈N there exists βk>0 such that this system has at least k sign-changing solutions (i.e., both two components change sign) and k semi-nodal solutions (i.e., one component changes sign and the other one is positive) for each fixed β∈(0, βk). © 2013 Elsevier Inc.
Type
journal article