Dancer-Fucik spectrum for fractional Schrodinger operators with a steep potential well on R-N

doi:10.1016/j.na.2019.06.024

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	Dancer-Fucik spectrum for fractional Schrodinger operators with a steep potential well on R-N
	Liu, Zhisu 1; Luo, Haijun 2; Zhang, Zhitao3,4
	2019-12-01
发表期刊	NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
ISSN	0362-546X
卷号	189 页码:26
摘要	In this paper, we study Dancer-Fubik spectrum of the fractional Schrodinger operators which is defined as the set of (alpha, beta) is an element of R-2 such that (-Delta)(s) u + V-lambda(x)u = alpha u(+) + beta u(-) in R-N has a nontrivial solution u, where the potential V-lambda has a steep potential well for sufficiently large parameter lambda > 0. It is allowed that (-Delta)(s) + V-lambda has essential spectrum with finitely many eigenvalues below the infimum of sigma(ess) ((-Delta)(s) + V-lambda). Many difficulties are caused by general nonlocal operators, we develop new techniques to overcome them to construct the first nontrivial curve of Dancer-Fucik point spectrum by minimax methods, to show some qualitative properties of the curve, and to prove that the corresponding eigenfunctions are foliated Schwartz symmetric. As applications we obtain the existence of nontrivial solutions for nonlinear Schrodinger equations with nonresonant nonlinearity. (C) 2019 Elsevier Ltd. All rights reserved.
关键词	Dancer-Fucik point spectrum Fractional Schrodinger operators Foliated Schwartz symmetric Nonresonance
DOI	10.1016/j.na.2019.06.024
语种	英语
资助项目	National Natural Science Foundation of China[11771428] ; National Natural Science Foundation of China[1170126] ; Natural Science Foundation of Hunan Province[2017JJ3265] ; Fundamental Research Funds for the Central Universities[531118010205]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000490149800006
出版者	PERGAMON-ELSEVIER SCIENCE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/35910
专题	数学所
通讯作者	Zhang, Zhitao
作者单位	1.Univ South China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China 2.Hunan Univ, Coll Math & Econometr, Changsha 410082, Hunan, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, HCMS, HLM,CEMS, Beijing 100190, Peoples R China 4.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Liu, Zhisu,Luo, Haijun,Zhang, Zhitao. Dancer-Fucik spectrum for fractional Schrodinger operators with a steep potential well on R-N[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS,2019,189:26.
APA	Liu, Zhisu,Luo, Haijun,&Zhang, Zhitao.(2019).Dancer-Fucik spectrum for fractional Schrodinger operators with a steep potential well on R-N.NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS,189,26.
MLA	Liu, Zhisu,et al."Dancer-Fucik spectrum for fractional Schrodinger operators with a steep potential well on R-N".NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 189(2019):26.