Multi-bump standing waves with a critical frequency for nonlinear Schrodinger equations
文献类型：期刊论文
| 作者 | Cao, DM ; Noussair, ES
|
| 刊名 | JOURNAL OF DIFFERENTIAL EQUATIONS
 |
| 出版日期 | 2004-09-01 |
| 卷号 | 203期号:2页码:292-312 |
| 关键词 | multi-bump standing waves variational method nonlinear Schrodinger equation |
| ISSN号 | 0022-0396 |
| DOI | 10.1016/j.jde.2004.05.003 |
| 英文摘要 | In this paper we study the existence and qualitative property of standing wave solutions psi(x, t) = e(-iEt/h) u(x) for the nonlinear Schrodinger equation ih(partial derivativepsi)/(partial derivativet) + (h2)/(2m) Deltapsi - W(x)psi + \psi\(p-1) = 0 with E being a critical frequency in the sense that inf(xis an element ofRN) W(x) E. We show that if the zero set of W - E has several isolated connected components Z(i)(i = 1,..., m) such that the interior of Z(i) is not empty and partial derivativeZ(i) is smooth, then for h > 0 small there exists, for any integer k, 1less than or equal tokless than or equal tom, a standing wave solution which is trapped in a neighborhood U-j=1(k) A(j), where {A(j)\ j = 1,..., k} is any given subset of {Z(i) \ i = 1,..., m}. Moreover the amplitude of the standing wave is of the level h(2/p-1). This extends the result of Byeon and Wang (Arch. Rational Mech. Anal. 165 (2002) 295) and is in striking contrast with the non-critical frequency case inf(xis an element ofRN) W(x) > E, which has been studied extensively in the past 20 years. (C) 2004 Elsevier Inc. All rights reserved. |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000222979500005 |
| 出版者 | ACADEMIC PRESS INC ELSEVIER SCIENCE |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/518]  |
| 专题 | 应用数学研究所 |
| 通讯作者 | Cao, DM |
| 作者单位 | 1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Appl Math, Beijing 100080, Peoples R China 2.Univ New S Wales, Sch Math, Sydney, NSW 2052, Australia |
| 推荐引用方式 GB/T 7714 | Cao, DM,Noussair, ES. Multi-bump standing waves with a critical frequency for nonlinear Schrodinger equations[J]. JOURNAL OF DIFFERENTIAL EQUATIONS,2004,203(2):292-312. |
| APA | Cao, DM,&Noussair, ES.(2004).Multi-bump standing waves with a critical frequency for nonlinear Schrodinger equations.JOURNAL OF DIFFERENTIAL EQUATIONS,203(2),292-312. |
| MLA | Cao, DM,et al."Multi-bump standing waves with a critical frequency for nonlinear Schrodinger equations".JOURNAL OF DIFFERENTIAL EQUATIONS 203.2(2004):292-312. |
入库方式： OAI收割
来源：数学与系统科学研究院
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