Asymptotic behaviour of ground state solutions for the Henon equation

doi:10.1093/imamat/hxn035

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	Asymptotic behaviour of ground state solutions for the Henon equation
	Cao, Daomin2 ; Peng, Shuangjie 1; Yan, Shusen 3
	2009-06-01
发表期刊	IMA JOURNAL OF APPLIED MATHEMATICS
ISSN	0272-4960
卷号	74 期号:3 页码:468-480
摘要	Let B(1)(0) subset of R(N) be the unit ball centred at the origin, N >= 3. In this paper, we analyse the profile of the ground state solution of the Henon equation - Delta u = \|x\|(alpha)u(p-1) in B(1)(0), u = 0 on partial derivative B(1)(0). We prove that for fixed p is an element of (2, 2()), (2() = 2N/(N - 2)), the maximum point x(alpha) of the ground state solution u(alpha) satisfies alpha(1 - vertical bar x(alpha)vertical bar) -> l is an element of (0, +infinity) as alpha -> infinity. We also obtain the asymptotic behaviour of u(alpha), which shows that the ground state solution is non-radial. Moreover, we prove the existence of multi-peaked solutions and give their asymptotic behaviour.
关键词	Henon equation ground state solutions asymptotic behaviour
DOI	10.1093/imamat/hxn035
语种	英语
资助项目	National Natural Science Foundation of China[10631030] ; National Natural Science Foundation of China[10721101] ; Chinese Academy of Sciences[KJCX3-SYW-S03] ; New Century Excellent Talents in University[07-0350] ; Key Project of Chinese Ministry of Education[107081] ; Scientific Research Foundation ; Australian Research Council of Australia
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000266499300010
出版者	OXFORD UNIV PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/8879
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, Beijing 100190, Peoples R China 3.Univ New England, Sch Math Stat & Comp Sci, Armidale, NSW 2351, Australia
推荐引用方式 GB/T 7714	Cao, Daomin,Peng, Shuangjie,Yan, Shusen. Asymptotic behaviour of ground state solutions for the Henon equation[J]. IMA JOURNAL OF APPLIED MATHEMATICS,2009,74(3):468-480.
APA	Cao, Daomin,Peng, Shuangjie,&Yan, Shusen.(2009).Asymptotic behaviour of ground state solutions for the Henon equation.IMA JOURNAL OF APPLIED MATHEMATICS,74(3),468-480.
MLA	Cao, Daomin,et al."Asymptotic behaviour of ground state solutions for the Henon equation".IMA JOURNAL OF APPLIED MATHEMATICS 74.3(2009):468-480.