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Some remarks on the critical point theory
Li, Chong
2007-12-01
Source PublicationTOPOLOGICAL METHODS IN NONLINEAR ANALYSIS
ISSN1230-3429
Volume30Issue:2Pages:223-234
AbstractIn this paper we discuss some problems about critical point theory. In the first part of the paper we study existence and multiplicity results of semilinear second order elliptic equation: [GRAPHICS] In [4], the authors study the contractibility of level sets of functionals associated with some elliptic boundary value problems. In this paper by using Morse theory and minimax method we give a more precise description of topological construction of level set of critical value of energy functional for mountain pass type critical point. It is well known that nondegenerate critical point is isolated, so if a critical point is not isolated, it must be a degenerate critical point. In the second part we will give an example that all the critical points of functional of a class of oscillating equation with Neumann boundary condition are isolated and the equation has only constant solutions. Moreover, critical groups of each critical point of the functional are trivial. The elliptic sine-Gordon equation originates from the static case of the hyperbolic sine-Gordon equation modelling the Josephson junction in superconductivity, which is of contemporary interest to physicists. The problem is similar to the elliptic sine-Gordon equation so we believe that it derives from profound physical backdrop.
Keywordmountain pass theorem order intervals Morse theory minimax method
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000251939000002
PublisherJULIUSZ SCHAUDER CTR NONLINEAR STUDIES
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/5096
Collection数学所
Corresponding AuthorLi, Chong
AffiliationAcad Sinica, AMSS, Inst Math, Beijing 100080, Peoples R China
Recommended Citation
GB/T 7714
Li, Chong. Some remarks on the critical point theory[J]. TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS,2007,30(2):223-234.
APA Li, Chong.(2007).Some remarks on the critical point theory.TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS,30(2),223-234.
MLA Li, Chong."Some remarks on the critical point theory".TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS 30.2(2007):223-234.
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