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 Publication | NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS |
ISSN | 0362-546X |
Volume | 189Pages:26 |
Abstract | 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. |
Keyword | Dancer-Fucik point spectrum Fractional Schrodinger operators Foliated Schwartz symmetric Nonresonance |
DOI | 10.1016/j.na.2019.06.024 |
Language | 英语 |
Funding Project | 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 Research Area | Mathematics |
WOS Subject | Mathematics, Applied ; Mathematics |
WOS ID | WOS:000490149800006 |
Publisher | PERGAMON-ELSEVIER SCIENCE LTD |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/35910 |
Collection | 数学所 |
Corresponding Author | Zhang, Zhitao |
Affiliation | 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 |
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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