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...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2011-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/326052 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832566205806804992 |
|---|---|
| author | A. Rontó M. Rontó |
| author_facet | A. Rontó M. Rontó |
| author_sort | A. Rontó |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-5a76438d0a03452aaf8fcf6d4013ff9a |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-5a76438d0a03452aaf8fcf6d4013ff9a2025-02-03T01:04:45ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/326052326052On Nonseparated Three-Point Boundary Value Problems for Linear Functional Differential EquationsA. Rontó0M. Rontó1Institute of Mathematics, Academy of Sciences of the Czech Republic, 22 Žižkova St., 61662 Brno, Czech RepublicDepartment of Analysis, University of Miskolc, 3515 Miskolc-Egyetemváros, HungaryFor 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.http://dx.doi.org/10.1155/2011/326052 |
| spellingShingle | A. Rontó M. Rontó On Nonseparated Three-Point Boundary Value Problems for Linear Functional Differential Equations Abstract and Applied Analysis |
| title | On Nonseparated Three-Point Boundary Value Problems for Linear Functional Differential Equations |
| title_full | On Nonseparated Three-Point Boundary Value Problems for Linear Functional Differential Equations |
| title_fullStr | On Nonseparated Three-Point Boundary Value Problems for Linear Functional Differential Equations |
| title_full_unstemmed | On Nonseparated Three-Point Boundary Value Problems for Linear Functional Differential Equations |
| title_short | On Nonseparated Three-Point Boundary Value Problems for Linear Functional Differential Equations |
| title_sort | on nonseparated three point boundary value problems for linear functional differential equations |
| url | http://dx.doi.org/10.1155/2011/326052 |
| work_keys_str_mv | AT aronto onnonseparatedthreepointboundaryvalueproblemsforlinearfunctionaldifferentialequations AT mronto onnonseparatedthreepointboundaryvalueproblemsforlinearfunctionaldifferentialequations |