Multi-bump bound states of Schrodinger equations with a critical frequency

doi:10.1007/s00208-006-0021-y

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	Multi-bump bound states of Schrodinger equations with a critical frequency
	Cao, Daomin; Peng, Shuangjie
	2006-12-01
发表期刊	MATHEMATISCHE ANNALEN
ISSN	0025-5831
卷号	336 期号:4 页码:925-948
摘要	We consider existence and qualitative properties of standing wave solutions psi(x,t) = e-(iEt/h)u( x) to the nonlinear Schr"dinger equation ih(partial derivative psi)/(partial derivative t) = -h(2)/2m Delta psi + W(x)psi - vertical bar psi vertical bar(p-1)psi =0 with E being a critical frequency in the sense that inf(x is an element of R)(N) W(x) = E. We verify that if the zero set of W - E has several isolated points x(i) (i = 1,..., m) near which W-E is almost exponentially flat with approximately the same behavior, then for h > 0 small enough, there exists, for any integer k, 1 <= k <= m, a standing wave solution which concentrates simultaneously on {x(j)vertical bar j = 1,..., k}, where {x(j)vertical bar j = 1,..., k} is any given subset of {x(j)vertical bar j = 1,..., k}. This generalizes the result of Byeon and Wang in 3.
关键词	multi-bump standing waves variational method nonlinear Schrodinger equation bound states
DOI	10.1007/s00208-006-0021-y
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000241379900006
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/3732
专题	应用数学研究所
通讯作者	Cao, Daomin
作者单位	1.Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China 2.Chinese Acad Sci, Inst Appl Math, AMSS, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Cao, Daomin,Peng, Shuangjie. Multi-bump bound states of Schrodinger equations with a critical frequency[J]. MATHEMATISCHE ANNALEN,2006,336(4):925-948.
APA	Cao, Daomin,&Peng, Shuangjie.(2006).Multi-bump bound states of Schrodinger equations with a critical frequency.MATHEMATISCHE ANNALEN,336(4),925-948.
MLA	Cao, Daomin,et al."Multi-bump bound states of Schrodinger equations with a critical frequency".MATHEMATISCHE ANNALEN 336.4(2006):925-948.