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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Veröffentlicht in:Journal of difference equations and applications Jg. 8; H. 5; S. 447 - 466
Hauptverfasser: Etheridge, Debra L., Rodriguez, Jesu´s
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Taylor & Francis Group 01.05.2002
Schlagworte:
Boundary Value Problems
Difference Equations
Implicit Function Theorem
Resonance
ISSN:1023-6198, 1563-5120
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Zusammenfassung: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.
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ISSN:1023-6198
1563-5120
DOI:10.1080/10236190290017432