Abstract and Applied Analysis
Volume 2011 (2011), Article ID 326052, 22 pages
Research Article

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

1Institute of Mathematics, Academy of Sciences of the Czech Republic, 22 Žižkova St., 61662 Brno, Czech Republic
2Department of Analysis, University of Miskolc, 3515 Miskolc-Egyetemváros, Hungary

Received 20 January 2011; Accepted 27 April 2011

Academic Editor: Yuri V. Rogovchenko

Copyright © 2011 A. Rontó and M. Rontó. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.