On nonseparated three-point boundary value problems for linear functional differential equations. (English) Zbl 1227.34067

Rontó, A.; Rontó, M.

Abstr. Appl. Anal. 2011, Article ID 326052, 22 p. (2011).

Summary: 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.

MSC:

34K10	Boundary value problems for functional-differential equations
34K06	Linear functional-differential equations
34K07	Theoretical approximation of solutions to functional-differential equations

Keywords:

parametric family of two-point boundary value problems; successive approximations

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