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

Pages from

1

Pages to

20

Pages count

20

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"
}