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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Vydané v:	Journal of difference equations and applications Ročník 8; číslo 5; s. 447 - 466
Hlavní autori:	Etheridge, Debra L., Rodriguez, Jesu´s
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Taylor & Francis Group 01.05.2002
Predmet:	Boundary Value Problems Difference Equations Implicit Function Theorem Resonance
ISSN:	1023-6198, 1563-5120
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Shrnutí:	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.
Bibliografia:	ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23
ISSN:	1023-6198 1563-5120
DOI:	10.1080/10236190290017432