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
	2017-11-15
发表期刊	JOURNAL OF DIFFERENTIAL EQUATIONS
ISSN	0022-0396
卷号	263 期号:10 页码:7000-7097
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.
关键词	Schrodinger equation Minimax principle Morse theory Maximum principle Exact homology sequences
DOI	10.1016/j.jde.2017.07.038
语种	英语
资助项目	NSFC[11471319] ; BCMIIS (Beijing Center for Mathematics and Information Interdisciplinary Sciences)
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000411303600025
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/26695
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.