Publication detail

The asymptotic properties of solutions of linear delay differential equations

KUNDRÁT, P.

Czech title

Asymptotické vlastnosti řešení diferenciálních rovnic se zpožděním

English title

The asymptotic properties of solutions of linear delay differential equations

Type

journal article - other

Language

en

Original abstract

The paper deals with the asymptotic behaviour of solutions of the delay differential equation x'(t)=a(t)x(t)+b(t)x(q(t))+f(t), t in [t0, infinity), where a is a positive function ond the ratio |b|/a can be estimated by means of a continuous and nonincreasing function. Some known asymptotic formulae concerning this equation are improved and extended to a more general case.

Czech abstract

Článek se zabývá asymptotickým chováním řešení zpožděné diferenciální rovnice x'(t)=a(t)x(t)+b(t)x(q(t))+f(t), t in [t0, infinity), kde a je kladná funkce a poměr |b|/a lze ohraničit spojitou nerostoucí funkcí. Jsou zde v jistém smyslu vylepšeny a zobecněny již známé asymptotické odhady řešení této rovnice.

English abstract

The paper deals with the asymptotic behaviour of solutions of the delay differential equation x'(t)=a(t)x(t)+b(t)x(q(t))+f(t), t in [t0, infinity), where a is a positive function ond the ratio |b|/a can be estimated by means of a continuous and nonincreasing function. Some known asymptotic formulae concerning this equation are improved and extended to a more general case.

Keywords in English

delay differential equation, functional equation, asymptotic behaviour

RIV year

2006

Released

15.08.2006

Publisher

Mathematical Institute of the Slovak Academy of Sciences

Location

Bratislava

ISSN

0139-9918

Journal

Mathematica Slovaca

Volume

56

Number

3

Pages from–to

349–360

Pages count

12

BIBTEX


@article{BUT43300,
  author="Petr {Tomášek},
  title="The asymptotic properties of solutions of linear delay differential equations",
  journal="Mathematica Slovaca",
  year="2006",
  volume="56",
  number="3",
  month="August",
  pages="349--360",
  publisher="Mathematical Institute of the Slovak Academy of Sciences",
  address="Bratislava",
  issn="0139-9918"
}