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Gaps of consecutive eigenvalues of Laplace operator and the existence of multiple solutions for superlinear elliptic problem

文献类型：期刊论文

作者Li, Chong1,2; Li, Shujie1,3
刊名JOURNAL OF FUNCTIONAL ANALYSIS
出版日期2016-07-15
卷号271期号:2页码:245-263
关键词New homological linking theorem The gaps of consecutive eigenvalues The fourth nontrivial solution Ambrosetti-Rabinowitz condition
ISSN号0022-1236
DOI10.1016/j.jfa.2016.04.020
英文摘要This paper is mainly related to multiple nontrivial solutions of the elliptic boundary value problem {-Delta u=vertical bar u vertical bar(p-2) u + f(x, u), x is an element of Omega, u=0, x is an element of partial derivative Omega, for p is an element of (2,2*). It is reasonable to guess that for dim Omega >= 2 above problem possesses infinitely many distinct solutions since this is proved to be true for ODE. However, so far one does not even know if there exists a fourth nontrivial solution. By using a new homological linking theorem, Morse theory, and some precise estimates we disclose the relationship among the gaps of consecutive eigenvalues of Laplace operator, growth trend of nonlinear terms and the existence of multiple solutions of superlinear elliptic boundary value problem. Moreover, as p is close to 2, we get the fourth nontrivial solution under appropriate hypotheses, where f (x, u) satisfies Ambrosetti-Rabinowitz condition. (C) 2016 Published by Elsevier Inc.
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:000377831100001
出版者ACADEMIC PRESS INC ELSEVIER SCIENCE
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/22900]  
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
3.Harbin Normal Univ, Yuan Rong Zeng Funct Anal Res Ctr, Harbin 150025, Peoples R China
推荐引用方式
GB/T 7714		 Li, Chong,Li, Shujie. Gaps of consecutive eigenvalues of Laplace operator and the existence of multiple solutions for superlinear elliptic problem[J]. JOURNAL OF FUNCTIONAL ANALYSIS,2016,271(2):245-263.
APA Li, Chong,&Li, Shujie.(2016).Gaps of consecutive eigenvalues of Laplace operator and the existence of multiple solutions for superlinear elliptic problem.JOURNAL OF FUNCTIONAL ANALYSIS,271(2),245-263.
MLA Li, Chong,et al."Gaps of consecutive eigenvalues of Laplace operator and the existence of multiple solutions for superlinear elliptic problem".JOURNAL OF FUNCTIONAL ANALYSIS 271.2(2016):245-263.

入库方式： OAI收割

来源：数学与系统科学研究院

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