On Nonseparated Three-Point Boundary Value Problems for Linear Functional Differential Equations
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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/326052 |
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| 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. |
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| ISSN: | 1085-3375 1687-0409 |