Publication detail

Asymptotic upper and lower estimates of a class of positive solutions of a discrete linear equation with a single delay

DIBLÍK, J. HLAVIČKOVÁ, I.

Original Title

Asymptotic upper and lower estimates of a class of positive solutions of a discrete linear equation with a single delay

English Title

Asymptotic upper and lower estimates of a class of positive solutions of a discrete linear equation with a single delay

Type

journal article - other

Language

en

Original Abstract

We study a frequently investigated class of linear difference equations with a positive coefficient p(n) and a single delay k. Recently, it was proved that if the function p(n) is bounded above by a certain function, then there exists a positive vanishing solution of the considered equation, and the upper bound was found. Here we improve this result by finding even the lower bound for the positive solution, supposing the function p(n) is bounded above and below by certain functions.

English abstract

We study a frequently investigated class of linear difference equations with a positive coefficient p(n) and a single delay k. Recently, it was proved that if the function p(n) is bounded above by a certain function, then there exists a positive vanishing solution of the considered equation, and the upper bound was found. Here we improve this result by finding even the lower bound for the positive solution, supposing the function p(n) is bounded above and below by certain functions.

Keywords

delayed difference equation; asymptotic estimates

RIV year

2012

Released

15.06.2012

ISBN

1085-3375

Periodical

Abstract and Applied Analysis

Year of study

2012

Number

ArticleID 764351

State

US

Pages from

1

Pages to

12

Pages count

12

URL

Documents

BibTex


@article{BUT92036,
  author="Josef {Diblík} and Irena {Hlavičková}",
  title="Asymptotic upper and lower estimates of a class of positive solutions of a discrete linear equation with a single delay",
  annote="We study a frequently investigated class of linear difference equations with a positive coefficient p(n) and a single delay k. Recently, it was proved that if the function p(n) is bounded above by a certain function, then there exists a positive vanishing solution of the considered equation, and the upper bound was found. Here we improve this result by finding even the lower bound for the positive solution, supposing the function p(n) is bounded above and below by certain functions.",
  chapter="92036",
  number="ArticleID 764351",
  volume="2012",
  year="2012",
  month="june",
  pages="1--12",
  type="journal article - other"
}