Concentration behavior of standing waves for almost mass critical nonlinear Schrodinger equations

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:256

Article

Guo, Yujin¹  Zeng, Xiaoyu¹  Zhou, Huan-Song¹ 

[1] Chinese Acad Sci, Wuhan Inst Phys & Math, Wuhan 430071, Peoples R China

关键词: Constrained variational method;    Energy estimates;    Concentration;    Standing waves;    Nonlinear Schrodinger equation;    Symmetry breaking;   

DOI  :  10.1016/j.jde.2013.12.012

来源: Elsevier

【 摘 要 】

We study the following nonlinear Schrodinger equation iu(t) = -Delta u + V(x)u - a vertical bar u vertical bar(q)u, (t,x) epsilon R-1 x R-2, where a > 0, q epsilon (0, 2), and V(x) is some type of trapping potential. For any fixed a > a* := parallel to Q parallel to(2)(2), where Q is the unique (up to translations) positive radial solution of Delta u - u + u(3) = 0 in R-2, by directly using constrained variational method and energy estimates we present a detailed analysis of the concentration and symmetry breaking of standing waves for the above equation as q NE arrow 2. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

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