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Existence of Multiple Solutions of a Second-Order Difference Boundary Value Problem
Joint Authors
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2010, Issue 2010 (31 Dec. 2010), pp.1-21, 21 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2010-03-22
Country of Publication
Egypt
No. of Pages
21
Main Subjects
Abstract EN
This paper studies the existence of multiple solutions of the second-order difference boundary value problem Δ2u(n−1)+V′(u(n))=0, n∈ℤ(1,T), u(0)=0=u(T+1).
By applying Morse theory, critical groups, and the mountain pass theorem, we prove that the previous equation has at least three nontrivial solutions when the problem is resonant at the eigenvalue λk (k≥2) of linear difference problem Δ2u(n−1)+λu(n)=0, n∈ℤ(1,T), u(0)=0=u(T+1) near infinity and the trivial solution of the first equation is a local minimizer under some assumptions on V.
American Psychological Association (APA)
Zheng, Bo& Xiao, Huafeng. 2010. Existence of Multiple Solutions of a Second-Order Difference Boundary Value Problem. International Journal of Mathematics and Mathematical Sciences،Vol. 2010, no. 2010, pp.1-21.
https://search.emarefa.net/detail/BIM-507135
Modern Language Association (MLA)
Zheng, Bo& Xiao, Huafeng. Existence of Multiple Solutions of a Second-Order Difference Boundary Value Problem. International Journal of Mathematics and Mathematical Sciences No. 2010 (2010), pp.1-21.
https://search.emarefa.net/detail/BIM-507135
American Medical Association (AMA)
Zheng, Bo& Xiao, Huafeng. Existence of Multiple Solutions of a Second-Order Difference Boundary Value Problem. International Journal of Mathematics and Mathematical Sciences. 2010. Vol. 2010, no. 2010, pp.1-21.
https://search.emarefa.net/detail/BIM-507135
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-507135