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- W2019918323 abstract "Motivated by problems arising in nonlinear optics and Bose–Einstein condensates, we consider in R N , with N ⩽ 3 , the following system of coupled Schrödinger equations: { − Δ u i + λ V i ( x ) u i = u i ∑ j = 1 d α i j u j 2 , u i ⩾ 0 , lim | x | → ∞ u i ( x ) = 0 , i = 1 , … , d , where λ > 0 is a parameter, α i j = α j i are positive constants, and V i non-negative given potentials. We assume that the interior of ⋂ i = 1 d V i − 1 ( 0 ) admits m connected components Ω 1 , … , Ω m which are of class C 1 , and isolated in each V i − 1 ( 0 ) . For each non-empty J ⊂ { 1 , … , m } , we prove that the system admits for any λ large a multi-bump solution u λ : R N → R d which is small in R N ∖ ⋃ j ∈ J Ω j , and on each Ω j ( j ∈ J ) close in H 1 -norm to a least energy solution of the limit problem: − Δ u i = u i ∑ j = 1 d α i j u j 2 , i = 1 , … , d , subjected to homogeneous Dirichlet boundary condition. An explicit condition on the matrix ( α i j ) is given to ensure our solutions have at least two positive components." @default.
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- W2019918323 date "2012-03-01" @default.
- W2019918323 modified "2023-09-28" @default.
- W2019918323 title "Multi-bump bound states for a system of nonlinear Schrödinger equations" @default.
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- W2019918323 doi "https://doi.org/10.1016/j.jde.2011.11.017" @default.
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