Publication detail
Boundary Value Problems for Delay Differential Systems
DIBLÍK, J. KHUSAINOV, D. RŮŽIČKOVÁ, M. BOICHUK, A.
Original Title
Boundary Value Problems for Delay Differential Systems
English Title
Boundary Value Problems for Delay Differential Systems
Type
journal article - other
Language
en
Original Abstract
Conditions are derived of the existence of solutions of linear Fredholms boundary-value problems for systems of ordinary differential equations with constant coefficients and a single delay, assuming that these solutions satisfy the initial and boundary conditions. Utilizing a delayed matrix exponential and a method of pseudoinverse by Moore-Penrose matrices led to an explicit and analytical form of a criterion for the existence of solutions in a relevant space and, moreover, to the construction of a family of linearly independent solutions of such problems in a general case with the number of boundary conditions (defined by a linear vector functional) not coinciding with the number of unknowns of a differential system with a single delay.
English abstract
Conditions are derived of the existence of solutions of linear Fredholms boundary-value problems for systems of ordinary differential equations with constant coefficients and a single delay, assuming that these solutions satisfy the initial and boundary conditions. Utilizing a delayed matrix exponential and a method of pseudoinverse by Moore-Penrose matrices led to an explicit and analytical form of a criterion for the existence of solutions in a relevant space and, moreover, to the construction of a family of linearly independent solutions of such problems in a general case with the number of boundary conditions (defined by a linear vector functional) not coinciding with the number of unknowns of a differential system with a single delay.
Keywords
linear Fredholms boundary-value problem, system of ordinary differential equations with constant coefficients and a single delay, delayed matrix exponential, Moore-Penrose matrices,
RIV year
2010
Released
16.07.2010
ISBN
1687-1839
Periodical
Advances in Difference Equations
Year of study
2010
Number
1
State
US
Pages from
1
Pages to
20
Pages count
20
Documents
BibTex
@article{BUT47944,
author="Josef {Diblík} and Denys {Khusainov} and Miroslava {Růžičková} and Alexander {Boichuk}",
title="Boundary Value Problems for Delay Differential Systems",
annote="Conditions are derived of the existence of solutions of linear Fredholms boundary-value problems for systems of ordinary differential equations with constant coefficients and a single delay,
assuming that these solutions satisfy the initial and boundary conditions. Utilizing a delayed
matrix exponential and a method of pseudoinverse by Moore-Penrose matrices led to an explicit and analytical form of a criterion for the existence of solutions in a relevant space and, moreover,
to the construction of a family of linearly independent solutions of such problems in a general case
with the number of boundary conditions (defined by a linear vector functional) not coinciding
with the number of unknowns of a differential system with a single delay.",
chapter="47944",
journal="Advances in Difference Equations",
number="1",
volume="2010",
year="2010",
month="july",
pages="1--20",
type="journal article - other"
}