Existence and uniqueness of multi-bump bound states of nonlinear Schrodinger equations with electromagnetic fields

doi:10.1016/j.jde.2005.06.027

CSpace > 应用数学研究所

	Existence and uniqueness of multi-bump bound states of nonlinear Schrodinger equations with electromagnetic fields
	Cao, DM; Tang, ZW
	2006-03-15
发表期刊	JOURNAL OF DIFFERENTIAL EQUATIONS
ISSN	0022-0396
卷号	222 期号:2 页码:381-424
摘要	In this paper, we are concerned with the existence and uniqueness of multi-bump bound states of the nonlinear Schrodinger equations with electromagnetic potential i (h) over bar partial derivative psi/partial derivative t = ((h) over bar /i del - A(x))(2) psi + V(x)psi - vertical bar psi vertical bar(p-2)psi, x is an element of R-N for sufficiently small h > 0, where i is the imaginary unit, 2 < p < 2N/N-2 for N >= 3 and 2 < p < + infinity for N = 1, 2. V(x) is a bonded real function on R-N, and A(x) = (A(1)(x), A(2)(x), ..., A(N)(x)) is such that A(j)(x) is a bounded real function on R-N for j 1,2, ..., N. For any finite collection of {a(1), a(2), ..., a(k)} of non-degenerate critical points of V(x), we show that there exists a solution psi(x, t) = exp(-iEt/h)u(x) which is a small perturbation of a sum of one-bump solutions concentrated at a(1), a(2), ..., a(k) and u(x) is unique up to rotations for small h > 0.
关键词	existence and uniqueness multi-bump bound states nonlinear Schrodinger equation magnetic fields
DOI	10.1016/j.jde.2005.06.027
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000235904100005
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/3762
专题	应用数学研究所
通讯作者	Cao, DM
作者单位	1.Chinese Acad Sci, AMSS, Inst Appl Math, Beijing 100080, Peoples R China 2.Beijing Normal Univ, Sch Math Sci, Beijing 100875, Peoples R China
推荐引用方式 GB/T 7714	Cao, DM,Tang, ZW. Existence and uniqueness of multi-bump bound states of nonlinear Schrodinger equations with electromagnetic fields[J]. JOURNAL OF DIFFERENTIAL EQUATIONS,2006,222(2):381-424.
APA	Cao, DM,&Tang, ZW.(2006).Existence and uniqueness of multi-bump bound states of nonlinear Schrodinger equations with electromagnetic fields.JOURNAL OF DIFFERENTIAL EQUATIONS,222(2),381-424.
MLA	Cao, DM,et al."Existence and uniqueness of multi-bump bound states of nonlinear Schrodinger equations with electromagnetic fields".JOURNAL OF DIFFERENTIAL EQUATIONS 222.2(2006):381-424.