The Fucik spectrum of Schrodinger operator and the existence of four solutions of Schrodinger equations with jumping nonlinearities

doi:10.1016/j.jde.2017.07.038

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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, Shujie 1
刊名	JOURNAL OF DIFFERENTIAL EQUATIONS
	2017-11-15
卷号	263 期号:10 页码:7000-7097
关键词	Schrodinger equation Minimax principle Morse theory Maximum principle Exact homology sequences
ISSN号	0022-0396
DOI	10.1016/j.jde.2017.07.038
英文摘要	This 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.
资助项目	NSFC[11471319] ; BCMIIS (Beijing Center for Mathematics and Information Interdisciplinary Sciences)
WOS研究方向	Mathematics
语种	英语
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
WOS记录号	WOS:000411303600025
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/26694]
专题	数学所
通讯作者	Li, Chong
作者单位	1.Acad Sinica, AMSS, Inst Math, Beijing 100190, Peoples R China 2.Beijing Ctr Math & Informat Interdisciplinary Sci, Beijing, Peoples R China
推荐引用方式 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.