Nonstandard solutions for a perturbed nonlinear Schrödinger system with small coupling coefficients

Abstract In this paper, we consider the following weakly coupled nonlinear Schrödinger system where , is a coupling constant, with if and if , V 1 and V 2 belong to . When and is suitably small, we show that the problem has a family of nonstandard solutions concentrating synchronously at the common...

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Bibliographic Details
Published inMathematische Nachrichten Vol. 294; no. 6; pp. 1052 - 1084
Main Authors An, Xiaoming, Wang, Chunhua
Format Journal Article
LanguageEnglish
Published Weinheim Wiley Subscription Services, Inc 01.06.2021
Subjects
Coupling coefficients
Decay rate
Variational methods
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Summary:Abstract In this paper, we consider the following weakly coupled nonlinear Schrödinger system where , is a coupling constant, with if and if , V 1 and V 2 belong to . When and is suitably small, we show that the problem has a family of nonstandard solutions concentrating synchronously at the common local minimum of V 1 and V 2 . All decay rates of are admissible and we can allow that is close to 0 in this paper. Moreover, the location of concentration points is given by local Pohozaev identities. Our proofs are based on variational methods and the penalized technique.
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.202000121