Multi-bump standing waves with a critical frequency for nonlinear Schrodinger equations

doi:10.1016/j.jde.2004.05.003

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	Multi-bump standing waves with a critical frequency for nonlinear Schrodinger equations
	Cao, DM; Noussair, ES
	2004-09-01
发表期刊	JOURNAL OF DIFFERENTIAL EQUATIONS
ISSN	0022-0396
卷号	203 期号:2 页码:292-312
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.
关键词	multi-bump standing waves variational method nonlinear Schrodinger equation
DOI	10.1016/j.jde.2004.05.003
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000222979500005
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/519
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.