Standing waves with prescribed mass for the Schrodinger equations with van der Waals type potentials

doi:10.1016/j.jde.2020.12.016

CSpace > 应用数学研究所

	Standing waves with prescribed mass for the Schrodinger equations with van der Waals type potentials
	Cao, Daomin1,2 ; Jia, Huifang 1; Luo, Xiao 3
	2021-03-05
发表期刊	JOURNAL OF DIFFERENTIAL EQUATIONS
ISSN	0022-0396
卷号	276 页码:228-263
摘要	In this paper, we focus on the standing waves with prescribed mass for the Schrodinger equations with van der Waals type potentials, that is, two-body potentials with different width. This leads to the study of the following nonlocal elliptic equation -Delta u = lambda u + mu(vertical bar x vertical bar(-alpha) * vertical bar u vertical bar(2))u+(vertical bar x vertical bar(-beta) * vertical bar u vertical bar(2))u, x is an element of R-N under the normalized constraint integral(RN) u(2) = c > 0, where N= 3, mu > 0, alpha, beta is an element of (0, N), and the frequency lambda is an element of R is unknown and appears as Lagrange multiplier. Compared with the well studied case alpha = beta, the solution set of the above problem with different width of two body potentials alpha not equal beta is much richer. Under different assumptions on c, alpha and beta, we prove several existence, multiplicity and asymptotic behavior of solutions to the above problem. In addition, the stability of the corresponding standing waves for the related time-dependent problem is discussed. (C) 2020 Elsevier Inc. All rights reserved.
关键词	Schrodinger equation vander Waals type potentials Normalized solutions Stability Variational methods
DOI	10.1016/j.jde.2020.12.016
收录类别	SCI
语种	英语
资助项目	NNSF of China[11771469] ; NNSF of China[12001126] ; NNSF of China[11771166] ; NNSF of China[11901147] ; Chinese Academy of Sciences[QYZDJSSW-SYS021] ; NPSF of China[2019M662833] ; Fundamental Research Funds for the Central Universities of China[JZ2019HGBZ0156] ; Fundamental Research Funds for the Central Universities of China[JZ2020HGTB0030]
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000606802700004
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/57986
专题	应用数学研究所
通讯作者	Jia, Huifang
作者单位	1.Guangzhou Univ, Sch Math & Informat Sci, Guangzhou 510405, Peoples R China 2.Chinese Acad Sci, Inst Appl Math, AMSS, Beijing 100190, Peoples R China 3.Hefei Univ Technol, Sch Math, Hefei 230009, Peoples R China
推荐引用方式 GB/T 7714	Cao, Daomin,Jia, Huifang,Luo, Xiao. Standing waves with prescribed mass for the Schrodinger equations with van der Waals type potentials[J]. JOURNAL OF DIFFERENTIAL EQUATIONS,2021,276:228-263.
APA	Cao, Daomin,Jia, Huifang,&Luo, Xiao.(2021).Standing waves with prescribed mass for the Schrodinger equations with van der Waals type potentials.JOURNAL OF DIFFERENTIAL EQUATIONS,276,228-263.
MLA	Cao, Daomin,et al."Standing waves with prescribed mass for the Schrodinger equations with van der Waals type potentials".JOURNAL OF DIFFERENTIAL EQUATIONS 276(2021):228-263.