On a class of five-point boundary value problems in second-order functional differential equations with parameter

1993 ◽  
Vol 62 (3-4) ◽  
pp. 253-262 ◽  
Author(s):  
S. Stanêk
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Functional Differential Equations ◽  
Second Order ◽  
Point Boundary ◽  
Functional Differential

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

2011 ◽  
Vol 2011 ◽  
pp. 1-22 ◽  
Author(s):  
A. Rontó ◽  
M. Rontó
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Linear Functional ◽  
Boundary Value ◽  
Functional Differential Equations ◽  
Special Kind ◽  
Successive Approximations ◽  
Point Problem ◽  
Point Boundary ◽  
Functional Differential

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.

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