Existence theorems for second-order discrete boundary value problems

This article is concerned with the existence of solutions of boundary value problems for nonlinear second-order difference equations of the type Δ [ p n ( Δ x n − 1 ) δ ] + q n x n δ = f ( n , x n ) , where δ > 0 is the ratio of odd positive integers, { p n } and { q n } are real sequences. The a...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2006-08, Vol.320 (2), p.649-661
Main Authors: Cai, Xiaochun, Yu, Jianshe
Format: Article
Language:English
Subjects:
Boundary value conditions
Difference equations
Exact sciences and technology
Finite differences and functional equations
Mathematical analysis
Mathematics
Sciences and techniques of general use
The Linking Theorem
The Mountain Pass Lemma
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Summary:This article is concerned with the existence of solutions of boundary value problems for nonlinear second-order difference equations of the type Δ [ p n ( Δ x n − 1 ) δ ] + q n x n δ = f ( n , x n ) , where δ > 0 is the ratio of odd positive integers, { p n } and { q n } are real sequences. The authors apply the Linking Theorem and the Mountain Pass Lemma in the critical point theory and give some new results for the existence of solutions.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2005.07.029