Abstract and Applied Analysis

On Nonseparated Three-Point Boundary Value Problems for Linear Functional Differential Equations

A. Rontó and M. Rontó

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Abstract

For a system of linear functional differential equations, we consider a three-point problem with nonseparated boundary conditions determined by singular matrices. We show that, to investigate such a problem, it is often useful to reduce it to a parametric family of two-point boundary value problems for a suitably perturbed differential system. The auxiliary parametrised two-point problems are then studied by a method based upon a special kind of successive approximations constructed explicitly, whereas the values of the parameters that correspond to solutions of the original problem are found from certain numerical determining equations. We prove the uniform convergence of the approximations and establish some properties of the limit and determining functions.

Article information

Source
Abstr. Appl. Anal., Volume 2011, Number 1 (2011), Article ID 326052, 22 pages.

Dates
First available in Project Euclid: 15 March 2012

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1331818380

Digital Object Identifier
doi:10.1155/2011/326052

Mathematical Reviews number (MathSciNet)
MR2822092

Zentralblatt MATH identifier
1227.34067

Citation

Rontó, A.; Rontó, M. On Nonseparated Three-Point Boundary Value Problems for Linear Functional Differential Equations. Abstr. Appl. Anal. 2011 (2011), no. 1, Article ID 326052, 22 pages. doi:10.1155/2011/326052. https://projecteuclid.org/euclid.aaa/1331818380


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