Properties of ground states of attractive Gross–Pitaevskii equations with multi-well potentials

doi:10.1088/1361-6544/aa99a8

	Properties of ground states of attractive Gross–Pitaevskii equations with multi-well potentials
	Wang,Zhi-Qiang 2,3; Zeng,Xiaoyu 4; Guo,Yujin 1; Zhou,Huan-Song 4
刊名	Nonlinearity
	2018-02-09
卷号	31 期号:3
关键词	ground states constrained variational problem Gross–Pitaevskii equation multi-well potential 36J20 35J60 35Q40
ISSN号	0951-7715
DOI	10.1088/1361-6544/aa99a8
英文摘要	Abstract We are interested in the attractive Gross–Pitaevskii (GP) equation in R2, where the external potential V(x) vanishes on m disjoint bounded domains Ωi?R2?(i=1,2,?,m) and V(x)→∞ as \|x\|→∞, that is, the union of these Ωi is the bottom of the potential well. By establishing some delicate estimates on the associated energy functional of the GP equation, we prove that when the interaction strength a approaches some critical value a?, the ground states concentrate and blow up at the center of the incircle of some Ωj with the largest inradius. Moreover, under some further conditions on V(x), we show that the ground states of the GP equations are unique and radially symmetric at least for almost every a∈(0,a?).
语种	英语
出版者	IOP Publishing
WOS记录号	IOP:0951-7715-31-3-AA99A8
内容类型	期刊论文
源URL	[http://ir.wipm.ac.cn/handle/112942/12350]
专题	中国科学院武汉物理与数学研究所
作者单位	1.Wuhan Institute of Physics and Mathematics, CAS, PO Box 71010, Wuhan 430071, People’s Republic of China 2.Center for Applied Mathematics, Tianjin University, 300072 Tianjin, People’s Republic of China 3.Department of Mathematics, Utah State University, Logan, UT 84322, United States of America 4.Center for Mathematical Sciences and Department of Mathematics, Wuhan University of Technology, Wuhan 430070, People’s Republic of China
推荐引用方式 GB/T 7714	Wang,Zhi-Qiang,Zeng,Xiaoyu,Guo,Yujin,et al. Properties of ground states of attractive Gross–Pitaevskii equations with multi-well potentials[J]. Nonlinearity,2018,31(3).
APA	Wang,Zhi-Qiang,Zeng,Xiaoyu,Guo,Yujin,&Zhou,Huan-Song.(2018).Properties of ground states of attractive Gross–Pitaevskii equations with multi-well potentials.Nonlinearity,31(3).
MLA	Wang,Zhi-Qiang,et al."Properties of ground states of attractive Gross–Pitaevskii equations with multi-well potentials".Nonlinearity 31.3(2018).