Semi-classical ground states concentrating on the nonlinear potential for a Dirac equation

doi:10.1016/j.jde.2010.03.022

CSpace > 数学所

	Semi-classical ground states concentrating on the nonlinear potential for a Dirac equation
	Ding, Yanheng1,2
	2010-09-01
发表期刊	JOURNAL OF DIFFERENTIAL EQUATIONS
ISSN	0022-0396
卷号	249 期号:5 页码:1015-1034
摘要	We study the semi-classical limit of the least energy solutions to the nonlinear Dirac equation -i epsilon Sigma(3)(k=1)alpha(k)partial derivative(k) + a beta u = P(x)vertical bar u vertical bar(p-2)u for x is an element of R-3. Since the Dirac operator is unbounded from below and above, the associate energy functional is strongly indefinite, and since the problem is considered in the global space R-3, the Palais-Smale condition is not satisfied. New phenomena and mathematical interests arise in the use of the calculus of variations. We prove that the equation has the least energy solutions for all epsilon > 0 small, and additionally these solutions converge to the least energy solutions of the associate limit problem and concentrate to the maxima of the nonlinear potential P(x) in certain sense as epsilon -> 0. (C) 2010 Elsevier Inc. All rights reserved.
关键词	Nonlinear Dirac equation Semi-classical states Concentration
DOI	10.1016/j.jde.2010.03.022
语种	英语
资助项目	National Natural Science Foundation of China[NSFC10831005] ; National Natural Science Foundation of China[10721061]
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000279292300001
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/10077
专题	数学所
通讯作者	Ding, Yanheng
作者单位	1.Chinese Acad Sci, Inst Math, AMSS, Beijing 100190, Peoples R China 2.Chinese Acad Sci, Hua Loo Keng Key Lab Math, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Ding, Yanheng. Semi-classical ground states concentrating on the nonlinear potential for a Dirac equation[J]. JOURNAL OF DIFFERENTIAL EQUATIONS,2010,249(5):1015-1034.
APA	Ding, Yanheng.(2010).Semi-classical ground states concentrating on the nonlinear potential for a Dirac equation.JOURNAL OF DIFFERENTIAL EQUATIONS,249(5),1015-1034.
MLA	Ding, Yanheng."Semi-classical ground states concentrating on the nonlinear potential for a Dirac equation".JOURNAL OF DIFFERENTIAL EQUATIONS 249.5(2010):1015-1034.