Weakly nonlinear discrete multipoint boundary value problems

In this paper we study nonlinear, discrete, multipoint boundary value problems of the form x ( t + 1 ) = A ( t ) x ( t ) + ϵ f ( t , x ( t ) ) subject to B 0 x ( 0 ) + B 1 x ( 1 ) + ⋯ + B N x ( N ) = 0 . We provide sufficient conditions for the existence of solutions and we present a qualitative ana...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 329; no. 1; pp. 77 - 91
Main Authors Rodriguez, Jesús, Taylor, Padraic
Format Journal Article
LanguageEnglish
Published San Diego, CA Elsevier Inc 01.05.2007
Elsevier
Subjects
Boundary value problems
Exact sciences and technology
Finite differences and functional equations
Implicit Function Theorem
Lyapunov–Schmidt
Mathematical analysis
Mathematics
Projection
Sciences and techniques of general use
Projection
Boundary value problems
Implicit Function Theorem
Lyapunov–Schmidt
Existence condition
Sufficient condition
Boundary value problem
Mathematical analysis
Existence of solution
Implicit function theorem
Qualitative analysis
Lyapunov-Schmidt
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Summary:In this paper we study nonlinear, discrete, multipoint boundary value problems of the form x ( t + 1 ) = A ( t ) x ( t ) + ϵ f ( t , x ( t ) ) subject to B 0 x ( 0 ) + B 1 x ( 1 ) + ⋯ + B N x ( N ) = 0 . We provide sufficient conditions for the existence of solutions and we present a qualitative analysis of the way the solutions depend on the parameter ϵ.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2006.06.024