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The Fucik spectrum of Schrodinger operator and the existence of four solutions of Schrodinger equations with jumping nonlinearities
Li, Chong1,2; Li, Shujie1
2017-11-15
Source PublicationJOURNAL OF DIFFERENTIAL EQUATIONS
ISSN0022-0396
Volume263Issue:10Pages:7000-7097
AbstractThis paper contains the existence of four solutions of Schrodinger equations with jumping nonlinearities. The proof procedure is supported by a lot of new results. Initially, a consequence is rendered as a minimax principle on H-1 (RN), which allows us to achieve the feasibility verification of the (PS) condition. Furthermore, the constructions of minimal and maximal curves of Fueik spectrum in Q(l) (see the introduction for the definition of Q(l)) warrant an intensive investigation. That we encounter some thorny problems is largely due to the absence of compact embedding and the appearance of essential spectrum. Based on a nontrivial argument, we can compute critical groups of homogeneous functional at zero if (a, b) is free of FueR spectrum and (a, b) is an element of Q(l). This together with convexity and concavity offers a detailed description of the two curves by a series of sophisticated tricks. Additionally, we present a new version of Morse theory in view of the fact that classical version doesn't work directly for weak smooth functional on H-1 (R-N). Finally, we prove a weak maximum principle for R-N, which serves as a tool to get a critical point in positive and negative cone respectively and also compute critical groups of critical points of mountain pass type. With the help of above preparations, we attain the ultimate aim by Morse inequalities and various exact homology sequences. (C) 2017 Elsevier Inc. All rights reserved.
KeywordSchrodinger equation Minimax principle Morse theory Maximum principle Exact homology sequences
DOI10.1016/j.jde.2017.07.038
Language英语
Funding ProjectNSFC[11471319] ; BCMIIS (Beijing Center for Mathematics and Information Interdisciplinary Sciences)
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000411303600025
PublisherACADEMIC PRESS INC ELSEVIER SCIENCE
Citation statistics
Cited Times:3[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/26695
Collection数学所
Affiliation1.Acad Sinica, AMSS, Inst Math, Beijing 100190, Peoples R China
2.Beijing Ctr Math & Informat Interdisciplinary Sci, Beijing, Peoples R China
Recommended Citation
GB/T 7714
Li, Chong,Li, Shujie. The Fucik spectrum of Schrodinger operator and the existence of four solutions of Schrodinger equations with jumping nonlinearities[J]. JOURNAL OF DIFFERENTIAL EQUATIONS,2017,263(10):7000-7097.
APA Li, Chong,&Li, Shujie.(2017).The Fucik spectrum of Schrodinger operator and the existence of four solutions of Schrodinger equations with jumping nonlinearities.JOURNAL OF DIFFERENTIAL EQUATIONS,263(10),7000-7097.
MLA Li, Chong,et al."The Fucik spectrum of Schrodinger operator and the existence of four solutions of Schrodinger equations with jumping nonlinearities".JOURNAL OF DIFFERENTIAL EQUATIONS 263.10(2017):7000-7097.
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