Detail publikačního výsledku

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

SVOBODA, Z.

Originální název

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

Anglický název

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

Druh

Článek Scopus

Originální abstrakt

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

Anglický abstrakt

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

Klíčová slova

representation of solutions; delay; matrix delayed functions.

Klíčová slova v angličtině

representation of solutions; delay; matrix delayed functions.

Autoři

SVOBODA, Z.

Rok RIV

2018

Vydáno

01.04.2017

Nakladatel

Springer New York LLC

Místo

New York US.

ISSN

1072-3374

Periodikum

Journal of Mathematical Sciences

Svazek

222

Číslo

3

Stát

Spojené státy americké

Strany od

345

Strany do

358

Strany počet

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"
}