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 |
| Summary: | 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. |
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| ISSN: | 1417-3875 |