Normalized solutions of mass subcritical Schrodinger equations in exterior domains

doi:10.1007/s00030-022-00764-5

CSpace

	Normalized solutions of mass subcritical Schrodinger equations in exterior domains
	Zhang, Zexin 1,2; Zhang, Zhitao 1,2,3
	2022-05-01
发表期刊	NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS
ISSN	1021-9722
卷号	29 期号:3 页码:25
摘要	In this paper, we study the nonlinear Schrodinger equation with L-2-norm constraint: {-Delta u = lambda u + vertical bar u vertical bar(p-2) u in Omega, u = 0 on partial derivative Omega, integral(Omega) vertical bar u vertical bar(2) dx = a(2), where N >= 3, Omega subset of R-N is an exterior domain, i.e., Omega is an unbounded domain with R-N\(Omega) over bar non-empty and bounded, a > 0, 2 < p < 2 + 4/N, and lambda is an element of R is Lagrange multiplier, which appears due to the mass constraint parallel to u parallel to(L2(Omega)) = a. We use Brouwer degree, barycentric functions and minimax method to prove that for any a > 0, there is a positive solution u is an element of H-0(1)(Omega) for some lambda < 0 if R-N\Omega is contained in a small ball. In addition, if we remove the restriction on Omega but impose that a > 0 is small, then we also obtain a positive solution u is an element of H-0(1)(Omega) for some lambda < 0. If Omega is the complement of unit ball in R-N, then for any a > 0, we get a positive radial solution u is an element of H-0(1) (Omega) for some lambda < 0 by Ekeland variational principle. Moreover, we use genus theory to obtain infinitely many radial solutions {(u(n), lambda(n))} with lambda(n) < 0, I-p(u(n)) < 0 for n >= 1 and I-p(u(n)) -> 0(-) as n -> infinity, where I-p is the corresponding energy functional.
关键词	Normalized solution Critical point Minimax theorem Schrodinger equation Exterior domain
DOI	10.1007/s00030-022-00764-5
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China[11771428] ; National Natural Science Foundation of China[12031015] ; National Natural Science Foundation of China[12026217] ; National Natural Science Foundation of China[11871302]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000777399600001
出版者	SPRINGER INT PUBL AG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/60210
专题	中国科学院数学与系统科学研究院
通讯作者	Zhang, Zexin
作者单位	1.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, HLM, Beijing 100190, Peoples R China 3.Jiangsu Univ, Sch Math Sci, Zhenjiang 212013, Peoples R China
推荐引用方式 GB/T 7714	Zhang, Zexin,Zhang, Zhitao. Normalized solutions of mass subcritical Schrodinger equations in exterior domains[J]. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS,2022,29(3):25.
APA	Zhang, Zexin,&Zhang, Zhitao.(2022).Normalized solutions of mass subcritical Schrodinger equations in exterior domains.NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS,29(3),25.
MLA	Zhang, Zexin,et al."Normalized solutions of mass subcritical Schrodinger equations in exterior domains".NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS 29.3(2022):25.