CSpace
Contractibility of level sets of functionals associated with some elliptic boundary value problems and applications
Liu, ZL; Li, SJ
2003
Source PublicationNODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS
ISSN1021-9722
Volume10Issue:2Pages:133-170
AbstractAssume that I is the functional defined on the Hilbert space H-0(1)(Omega) concerning the problem: -Deltau = f(u) in Omega and u = 0 on partial derivativeOmega, where f is sublinear at infinity and superlinear at 0, that is, lim sup(\t\ --> infinity) f (t)/t < lambda(1), lim inf(t-->0)f(t)/t > lambda(1), and lambda(1), is the first eigenvalue of -Delta in H-0(1)(Omega). Under very general conditions, I has at least two local minimizers u(1) and u(2) and one mountain pass point u(3), and max{I(u(1)), I(u(2))} < I(u(3)) < 0. Assuming that u(1), u(2) and u(3) are the only three nontrivial critical points of I, we prove that the level set I-b is contractible for all b greater than or equal to I (u(3)). Using this conclusion, we extend one of Hofer's result concerning existence of four nontrivial solutions of the above problem to the case where I is not C-2 and the trivial critical point 0 may be degenerate. Since I is not C-2, the local topological degree and the critical groups Of u(3) can not be clearly computed. The lack of topological information about 0 and u(3) makes it impossible to use topological degree theory or Morse theory in obtaining the fourth nontrivial solution. To overcome these difficulties, we explore a new technique in this paper. 2000 Mathematics Subject Classification: 35J20, 35J25.
Keywordcritical point elliptic boundary value problem jumping nonlinearity four nontrivial solutions contractibility of level set
DOI10.1007/S00030-003-1016-y
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000183520600001
PublisherBIRKHAUSER VERLAG AG
Citation statistics
Cited Times:2[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/18167
Collection中国科学院数学与系统科学研究院
Affiliation1.Shandong Univ, Dept Math, Jinan 250100, Shandong, Peoples R China
2.Acad Sinica, Acad Math & Syst Sci, Beijing 100080, Peoples R China
Recommended Citation
GB/T 7714
Liu, ZL,Li, SJ. Contractibility of level sets of functionals associated with some elliptic boundary value problems and applications[J]. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS,2003,10(2):133-170.
APA Liu, ZL,&Li, SJ.(2003).Contractibility of level sets of functionals associated with some elliptic boundary value problems and applications.NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS,10(2),133-170.
MLA Liu, ZL,et al."Contractibility of level sets of functionals associated with some elliptic boundary value problems and applications".NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS 10.2(2003):133-170.
Files in This Item:
There are no files associated with this item.
Related Services
Recommend this item
Bookmark
Usage statistics
Export to Endnote
Google Scholar
Similar articles in Google Scholar
[Liu, ZL]'s Articles
[Li, SJ]'s Articles
Baidu academic
Similar articles in Baidu academic
[Liu, ZL]'s Articles
[Li, SJ]'s Articles
Bing Scholar
Similar articles in Bing Scholar
[Liu, ZL]'s Articles
[Li, SJ]'s Articles
Terms of Use
No data!
Social Bookmark/Share
All comments (0)
No comment.
 

Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.