Semi-Classical Bound States for Schrodinger Equations with Potentials Vanishing or Unbounded at Infinity

doi:10.1080/03605300903346721

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	Semi-Classical Bound States for Schrodinger Equations with Potentials Vanishing or Unbounded at Infinity
	Cao, Daomin2 ; Peng, Shuangjie 1
	2009
发表期刊	COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS
ISSN	0360-5302
卷号	34 期号:12 页码:1566-1591
摘要	In this paper we study the existence and qualitative property of standing wave solutions [image omitted] for the nonlinear Schrodinger equation [image omitted]. Let [image omitted]. For any integer k epsilon 1, we prove existence of standing wave solutions with u0 having k local maximum points and concentrating near a given local maximum point of when epsilon is small. The potentials V and K are allowed to be either vanishing or unbounded at infinity. Existence of solutions concentrating near k distinct non-degenerate critical points of has been proved under the same assumptions on V and K as well.
关键词	Bound states Concentrating solutions Critical point Potential vanishing or unbounded at infinity Variational method
DOI	10.1080/03605300903346721
语种	英语
资助项目	Natural Science Foundation of China (NSFC)[10631030] ; Natural Science Foundation of China (NSFC)[10721101] ; Program for New Century Excellent Talents in University[07-0350] ; Chinese Ministry of Education[107081]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000274422000002
出版者	TAYLOR & FRANCIS INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/7539
专题	应用数学研究所
通讯作者	Peng, Shuangjie
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, Peoples R China
推荐引用方式 GB/T 7714	Cao, Daomin,Peng, Shuangjie. Semi-Classical Bound States for Schrodinger Equations with Potentials Vanishing or Unbounded at Infinity[J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS,2009,34(12):1566-1591.
APA	Cao, Daomin,&Peng, Shuangjie.(2009).Semi-Classical Bound States for Schrodinger Equations with Potentials Vanishing or Unbounded at Infinity.COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS,34(12),1566-1591.
MLA	Cao, Daomin,et al."Semi-Classical Bound States for Schrodinger Equations with Potentials Vanishing or Unbounded at Infinity".COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS 34.12(2009):1566-1591.