The Fucik spectrum of Schrodinger operator and the existence of four solutions of Schrodinger equations with jumping nonlinearities
文献类型：期刊论文
| 作者 | Li, Chong1,2 ; Li, Shujie1
|
| 刊名 | JOURNAL OF DIFFERENTIAL EQUATIONS
 |
| 出版日期 | 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 |
| WOS记录号 | WOS:000411303600025 |
| 出版者 | ACADEMIC PRESS INC ELSEVIER SCIENCE |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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