Fredholm boundary-value problems for linear delay systems defined by pairwise permutable matrices
The paper deals with a Fredholm boundary value problem for a linear delay system with several delays defined by pairwise permutable constant matrices. The initial value condition is given on a finite interval and the boundary condition is given by a linear vector functional. A sufficient condition f...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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University of Szeged
2015-05-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=3712 |
| _version_ | 1797830647094444032 |
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| author | Oleksandr Boichuk Milan Medved Valerii Zhuravliov |
| author_facet | Oleksandr Boichuk Milan Medved Valerii Zhuravliov |
| author_sort | Oleksandr Boichuk |
| collection | DOAJ |
| description | The paper deals with a Fredholm boundary value problem for a linear delay system with several delays defined by pairwise permutable constant matrices. The initial value condition is given on a finite interval and the boundary condition is given by a linear vector functional. A sufficient condition for the existence of solutions of this type of boundary value problem is proved. Moreover, a family of linearly independent solutions in an explicit general analytic form is constructed under the assumption that the number of boundary conditions (defined by a dimension of linear vector functional) do not coincide with the number of unknowns of the system of the delay differential equations. The proof of this result is based on a representation of solutions by using so-called multi-delayed matrix exponential and a method of a pseudo-inverse matrix of the Moore-Penrose type. |
| first_indexed | 2024-04-09T13:39:25Z |
| format | Article |
| id | doaj.art-64563c7f13664fe4852c60a0525c7547 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:39:25Z |
| publishDate | 2015-05-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-64563c7f13664fe4852c60a0525c75472023-05-09T07:53:04ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752015-05-012015231910.14232/ejqtde.2015.1.233712Fredholm boundary-value problems for linear delay systems defined by pairwise permutable matricesOleksandr Boichuk0Milan Medved1Valerii Zhuravliov2Institute of Mathematics NASUComenius University, Bratislava, SlovakiaZhitomyr National Agroecological University, UkraineThe paper deals with a Fredholm boundary value problem for a linear delay system with several delays defined by pairwise permutable constant matrices. The initial value condition is given on a finite interval and the boundary condition is given by a linear vector functional. A sufficient condition for the existence of solutions of this type of boundary value problem is proved. Moreover, a family of linearly independent solutions in an explicit general analytic form is constructed under the assumption that the number of boundary conditions (defined by a dimension of linear vector functional) do not coincide with the number of unknowns of the system of the delay differential equations. The proof of this result is based on a representation of solutions by using so-called multi-delayed matrix exponential and a method of a pseudo-inverse matrix of the Moore-Penrose type.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=3712boundary-value problemmulti-delayed systemmoore-penrose pseudo-inverse matrix. |
| spellingShingle | Oleksandr Boichuk Milan Medved Valerii Zhuravliov Fredholm boundary-value problems for linear delay systems defined by pairwise permutable matrices Electronic Journal of Qualitative Theory of Differential Equations boundary-value problem multi-delayed system moore-penrose pseudo-inverse matrix. |
| title | Fredholm boundary-value problems for linear delay systems defined by pairwise permutable matrices |
| title_full | Fredholm boundary-value problems for linear delay systems defined by pairwise permutable matrices |
| title_fullStr | Fredholm boundary-value problems for linear delay systems defined by pairwise permutable matrices |
| title_full_unstemmed | Fredholm boundary-value problems for linear delay systems defined by pairwise permutable matrices |
| title_short | Fredholm boundary-value problems for linear delay systems defined by pairwise permutable matrices |
| title_sort | fredholm boundary value problems for linear delay systems defined by pairwise permutable matrices |
| topic | boundary-value problem multi-delayed system moore-penrose pseudo-inverse matrix. |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=3712 |
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