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

doi:10.1016/j.jfa.2016.04.020

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	Gaps of consecutive eigenvalues of Laplace operator and the existence of multiple solutions for superlinear elliptic problem
	Li, Chong1,2 ; Li, Shujie 1,3
	2016-07-15
发表期刊	JOURNAL OF FUNCTIONAL ANALYSIS
ISSN	0022-1236
卷号	271 期号:2 页码:245-263
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.
关键词	New homological linking theorem The gaps of consecutive eigenvalues The fourth nontrivial solution Ambrosetti-Rabinowitz condition
DOI	10.1016/j.jfa.2016.04.020
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:000377831100001
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/22901
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.