Eigenvalue problem for a p-Laplacian equation with trapping potentials

CORC > 武汉物理与数学研究所 > 中国科学院武汉物理与数学研究所 > 数学物理与应用研究部

	Eigenvalue problem for a p-Laplacian equation with trapping potentials
	Gu, Long-Jiang 1; Zeng, Xiaoyu 2; Zhou, Huan-Song 2
刊名	NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
	2017
卷号	148 页码:212-227
关键词	P-Laplacian Elliptic equation Eigenvalue problem Least energy Blowup rate
英文摘要	Consider the following eigenvalue problem of p-Laplacian equation - Delta(P)u + V(x)vertical bar u vertical bar(p-2)u = mu vertical bar u vertical bar(p-2)u + a vertical bar u vertical bar(s-2)u, x epsilon R-n, (P) where a >= 0, p is an element of (1,n) and is an element of R. V(x) is a trapping type potential, e.g., inf(x)is an element of R-n. V(x) < lim(vertical bar x vertical bar ->+infinity) V(x). By using constrained variational methods, we proved that there is a* > 0, which can be given explicitly, such that problem (P) has a ground state u with vertical bar u vertical bar L-p = 1 for some mu is an element of R and all a is an element of [0, a), but (P) has no this kind of ground state if a >= a. Furthermore, by establishing some delicate energy estimates we show that the global maximum point of the ground state of problem (P) approaches one of the global minima of V(x) and blows up if a NE arrow a*. The optimal rate of blowup is obtained for V(x) being a polynomial type potential. (C) 2016 Elsevier Ltd. All rights reserved.
WOS标题词	Science & Technology ; Physical Sciences
类目[WOS]	Mathematics, Applied ; Mathematics
研究领域[WOS]	Mathematics
关键词[WOS]	LINEAR ELLIPTIC-EQUATIONS ; POSITIVE SOLUTIONS ; UNBOUNDED-DOMAINS ; GROUND-STATES ; UNIQUENESS ; EXISTENCE ; SYMMETRY ; RN ; PRINCIPLE ; R(N)
收录类别	SCI
语种	英语
WOS记录号	WOS:000389093500011
内容类型	期刊论文
源URL	[http://ir.wipm.ac.cn/handle/112942/9981]
专题	武汉物理与数学研究所_数学物理与应用研究部
作者单位	1.Chinese Acad Sci, Wuhan Inst Phys & Math, POB 71010, Wuhan 430071, Peoples R China 2.Wuhan Univ Technol, Dept Math, Wuhan 430070, Peoples R China
推荐引用方式 GB/T 7714	Gu, Long-Jiang,Zeng, Xiaoyu,Zhou, Huan-Song. Eigenvalue problem for a p-Laplacian equation with trapping potentials[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS,2017,148:212-227.
APA	Gu, Long-Jiang,Zeng, Xiaoyu,&Zhou, Huan-Song.(2017).Eigenvalue problem for a p-Laplacian equation with trapping potentials.NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS,148,212-227.
MLA	Gu, Long-Jiang,et al."Eigenvalue problem for a p-Laplacian equation with trapping potentials".NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 148(2017):212-227.