Article ID Journal Published Year Pages File Type
4610677 Journal of Differential Equations 2013 23 Pages PDF
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⊂RNΩ⊂RN (N=2,3N=2,3) is a smooth bounded domain, λ1,λ2λ1,λ2, μ1,μ2μ1,μ2 are all positive constants. We show that, for each k∈Nk∈N there exists βk>0βk>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)β∈(0,βk).

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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