On finding solutions of two-point boundary value problems for a class of non-linear functional differential systems

We consider the two-point boundary value problems for a certain class of nonlinear functional-differential equation. To study the problem, we use a method based upon a special type of successive approximations that are constructed analytically and, under suitable conditions, converge uniformly on th...

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Bibliographic Details
Published in:Electronic journal of qualitative theory of differential equations 2012-05, Vol.2012 (13), p.1-17
Main Authors: András Rontó, Miklós Rontó, Nataliya Shchobak
Format: Article
Language:English
Subjects:
convergence
existence
nonlinear functional-differential equation
special deviation of argument
successive approximations
two-point linear boundary conditions
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Summary:We consider the two-point boundary value problems for a certain class of nonlinear functional-differential equation. To study the problem, we use a method based upon a special type of successive approximations that are constructed analytically and, under suitable conditions, converge uniformly on the given interval. Our techniques lead one to a certain finite-dimensional system of numerical determining equations that "detect" all the solutions of the problem. Based on properties of these equations, we give efficient conditions ensuring the solvability of the original problem. The conditions are formulated in terms of functions that are potential candidates for approximate solutions and, being such, are constructed explicitly.
ISSN:1417-3875
DOI:10.14232/ejqtde.2012.3.13