Bound states of nonlinear Schrodinger equations with magnetic fields

doi:10.1007/s10231-010-0157-y

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	Bound states of nonlinear Schrodinger equations with magnetic fields
	Ding, Yanheng2 ; Wang, Zhi-Qiang 1
	2011-09-01
发表期刊	ANNALI DI MATEMATICA PURA ED APPLICATA
ISSN	0373-3114
卷号	190 期号:3 页码:427-451
摘要	We study bound states of the following nonlinear Schrodinger equation in the presence of a magnetic field: (- ih del + A(x))(2) u + V(x)u = g( x, \|u\|)u \|u\| is an element of H-1(R-N) where A : R-N -> R-N, V : R-N -> R-N R and g : R-N x R -> [0,infinity). We prove that if V is bounded below with the set {x. RN : V( x) < b} not equal phi having finite measure for some b > 0, inf V <= 0, and g satisfies some growth conditions, then for any integer m when h > 0 is sufficiently small the problem has m geometrically different solutions.
关键词	Nonlinear Schrodinger equation Magnetic fields Sign-changing potential Subcritical and supercritical growth
DOI	10.1007/s10231-010-0157-y
语种	英语
资助项目	National Natural Science Foundation of China
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000293922600004
出版者	SPRINGER HEIDELBERG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/11526
专题	数学所
通讯作者	Wang, Zhi-Qiang
作者单位	1.Utah State Univ, Dept Math & Stat, Logan, UT 84322 USA 2.Chinese Acad Sci, AMSS, Inst Math, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Ding, Yanheng,Wang, Zhi-Qiang. Bound states of nonlinear Schrodinger equations with magnetic fields[J]. ANNALI DI MATEMATICA PURA ED APPLICATA,2011,190(3):427-451.
APA	Ding, Yanheng,&Wang, Zhi-Qiang.(2011).Bound states of nonlinear Schrodinger equations with magnetic fields.ANNALI DI MATEMATICA PURA ED APPLICATA,190(3),427-451.
MLA	Ding, Yanheng,et al."Bound states of nonlinear Schrodinger equations with magnetic fields".ANNALI DI MATEMATICA PURA ED APPLICATA 190.3(2011):427-451.