On Perturbed Discrete Boundary Value Problems

In this paper, we study nonlinear discrete boundary value problems of the form x ( t +1)= A ( t ) x ( t )+ h ( t )+ k f ( t , x ( t ), k ) subject to Bx (0)+ Dx ( J )= u + k g ( x (0), x ( J ), k ) where k is a "small" parameter. Our main concern is the case of resonance, that is, the situ...

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Bibliographic Details
Published inJournal of difference equations and applications Vol. 8; no. 5; pp. 447 - 466
Main Authors Etheridge, Debra L., Rodriguez, Jesu´s
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 01.05.2002
Subjects
Boundary Value Problems
Difference Equations
Implicit Function Theorem
Resonance
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Summary:In this paper, we study nonlinear discrete boundary value problems of the form x ( t +1)= A ( t ) x ( t )+ h ( t )+ k f ( t , x ( t ), k ) subject to Bx (0)+ Dx ( J )= u + k g ( x (0), x ( J ), k ) where k is a "small" parameter. Our main concern is the case of resonance, that is, the situation where the associated linear homogeneous boundary value problem x ( t +1)= A ( t ) x ( t ), Bx (0)+ Dx ( J )=0 admits nontrivial solutions. We establish conditions for the solvability of the nonlinear boundary value problem when k is "small". We also establish qualitative properties of these solutions.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
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content type line 23
ISSN:1023-6198
1563-5120
DOI:10.1080/10236190290017432