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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Published in	Journal of mathematical analysis and applications Vol. 329; no. 1; pp. 77 - 91
Main Authors	Rodriguez, Jesús, Taylor, Padraic
Format	Journal Article
Language	English
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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ISSN	0022-247X 1096-0813
DOI	10.1016/j.jmaa.2006.06.024

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Abstract	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.
AbstractList	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.
Author	Rodriguez, Jesús Taylor, Padraic
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Snippet	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...
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SubjectTerms	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
Title	Weakly nonlinear discrete multipoint boundary value problems
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