Publication detail

Representation of Solutions of Linear Differential Systems of the Second Order with Constant Delays

SVOBODA, Z.

Original Title

Representation of Solutions of Linear Differential Systems of the Second Order with Constant Delays

Type

journal article in Scopus

Language

English

Original Abstract

We deduce representations for the solutions of initial-value problems for n-dimensional differential equations of the second order with delays:x″(t)=2Ax′(t−τ)−(A2+B2)x(t−2τ) and x″(t)=(A+B)x′(t−τ)−ABx(t−2τ) by using special delay matrix functions. Here, A and B are commuting (n × n)-matrices and τ > 0. Moreover, a formula connecting the delay matrix exponential function with delayed matrix sine and delayed matrix cosine is obtained. We also discuss common features of the considered equations

Keywords

representation of solutions; delay; matrix delayed functions.

Authors

SVOBODA, Z.

Released

1. 4. 2017

Publisher

Springer New York LLC

Location

New York US.

ISBN

1072-3374

Periodical

Journal of Mathematical Sciences

Year of study

222

Number

3

State

United States of America

Pages from

345

Pages to

358

Pages count

14

BibTex

@article{BUT143601,
  author="Zdeněk {Svoboda}",
  title="Representation of Solutions of Linear Differential Systems of the Second Order with Constant Delays",
  journal="Journal of Mathematical Sciences",
  year="2017",
  volume="222",
  number="3",
  pages="345--358",
  doi="10.1007/s10958-017-3304-9",
  issn="1072-3374"
}