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Dancer-Fucik spectrum for fractional Schrodinger operators with a steep potential well on R-N
Liu, Zhisu1; Luo, Haijun2; Zhang, Zhitao3,4
2019-12-01
Source PublicationNONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
ISSN0362-546X
Volume189Pages:26
AbstractIn 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.
KeywordDancer-Fucik point spectrum Fractional Schrodinger operators Foliated Schwartz symmetric Nonresonance
DOI10.1016/j.na.2019.06.024
Language英语
Funding ProjectNational 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 Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000490149800006
PublisherPERGAMON-ELSEVIER SCIENCE LTD
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/35910
Collection数学所
Corresponding AuthorZhang, Zhitao
Affiliation1.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
Recommended Citation
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.
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