SEGREGATED VECTOR SOLUTIONS FOR NONLINEAR SCHRÖDINGER SYSTEMS IN R2

doi:10.1016/S0252-9602(15)60010-8

Acta mathematica scientia,Series B ›› 2015, Vol. 35 ›› Issue (2): 383-398.doi: 10.1016/S0252-9602(15)60010-8

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SEGREGATED VECTOR SOLUTIONS FOR NONLINEAR SCHRÖDINGER SYSTEMS IN R²

Chunhua WANG, Dingyi XIE, Liping ZHAN, Lipan ZHANG, Liangpei ZHAO

School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China

Received:2013-05-07 Revised:2014-04-15 Online:2015-03-20 Published:2015-03-20
Contact: Chunhua WANG School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China E-mail: chunhuawang@mail.ccnu.edu.cn E-mail:chunhuawang@mail.ccnu.edu.cn
Supported by:
The authors sincerely thank Professor S. Peng for helpful discussions and suggestions. This work was partially supported by National College Students Innovation Training Project (48), the fund from NSFC (11301204), and the phD specialized grant of the Ministry of Education of China (20110144110001).

Abstract

Abstract:

We study the following nonlinear Schrödinger system

where P(r) and Q(r) are positive radial functions, μ >0,ν >0, and β∈R is a coupling constant. This type of system arises, particularly, in models in Bose-Einstein condensates theory. Applying a finite reduction method, we construct an unbounded sequence of nonradial positive vector solutions of segregated type when β is in some suitable interval, which gives an answer to an interesting problem raised by Peng and Wang in Remark 4.1 (Arch. Ration. Mech. Anal., 208(2013), 305-339).

Key words: Segregated vector solutions, nonlinear Schrö, dinger systems

CLC Number:

35J10

Chunhua WANG, Dingyi XIE, Liping ZHAN, Lipan ZHANG, Liangpei ZHAO. SEGREGATED VECTOR SOLUTIONS FOR NONLINEAR SCHRÖDINGER SYSTEMS IN R²[J].Acta mathematica scientia,Series B, 2015, 35(2): 383-398.

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SEGREGATED VECTOR SOLUTIONS FOR NONLINEAR SCHRÖDINGER SYSTEMS IN R²

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