Publication detail

Asymptotic properties of solutions of the difference equation \Delta x(t)=-ax(t)+bx(\tau(t))

KUNDRÁT, P.

Czech title

Asymptotické vlastnosti řešení diferenční rovnice \Delta x(t)=-ax(t)+bx(\tau(t))

English title

Asymptotic properties of solutions of the difference equation \Delta x(t)=-ax(t)+bx(\tau(t))

Type

conference paper

Language

en

Original abstract

In this paper we derive the asymptotic bounds of all solutions of the delay difference equation \Delta x(t)=-ax(t)+bx(\tau(t)), t\in[t_0,infinity) with real constants a>0, b\neq 0. This equation is obtained via the discretization of a delay differential equation and we show the resemblance in the asymptotic bounds of both equations.

Czech abstract

V tomto článku jsou odvozeny asymptotické odhady řešení zpožděné diferenční rovnice \Delta x(t)=-ax(t)+bx(\tau(t)), t\in[t_0,infinity), kde a,b jsou reálné konstanty splňující relace a>0, b\neq 0. Tato rovnice je diskretizací zpožděné diferenciální rovnice a je ukázána souvislost asymptotických odhadů obou rovnic.

English abstract

In this paper we derive the asymptotic bounds of all solutions of the delay difference equation \Delta x(t)=-ax(t)+bx(\tau(t)), t\in[t_0,infinity) with real constants a>0, b\neq 0. This equation is obtained via the discretization of a delay differential equation and we show the resemblance in the asymptotic bounds of both equations.

Keywords in Czech

diferenční rovnice, zpožděný argument, asymptotické chování

Keywords in English

difference equation, delayed argument, asymptotic behaviour

RIV year

2005

Released

01.01.2005

Publisher

Chapman & Hall

Location

Boca Raton

ISBN

1-58488-536-X

Book

Proceedings of the Eighth International Conference on Difference Equations and Applications

Pages count

8

BIBTEX


@inproceedings{BUT14717,
  author="Petr {Tomášek},
  title="Asymptotic properties of solutions of the difference equation \Delta x(t)=-ax(t)+bx(\tau(t))",
  booktitle="Proceedings of the Eighth International Conference on Difference Equations and Applications",
  year="2005",
  month="January",
  publisher="Chapman & Hall",
  address="Boca Raton",
  isbn="1-58488-536-X"
}