Publication detail

# Oscillation of solution of a linear third-order discrete delayed equation

DIBLÍK, J. BAŠTINCOVÁ, A. BAŠTINEC, J.

Original Title

Oscillation of solution of a linear third-order discrete delayed equation

English Title

Oscillation of solution of a linear third-order discrete delayed equation

Type

conference paper

Language

en

Original Abstract

A linear third-order discrete delayed equation $Delta x(n)=-p(n)x(n-2)$ with a positive coefficient $p$ is considered for $n$ going to $\infty$. This equation is known to have a positive solution if $p$ fulfils an inequality. The goal of the paper is to show that, in the case of the opposite inequality for $p$, all solutions of the equation considered are oscillating for $n$ tending to $\infty$.

English abstract

A linear third-order discrete delayed equation $Delta x(n)=-p(n)x(n-2)$ with a positive coefficient $p$ is considered for $n$ going to $\infty$. This equation is known to have a positive solution if $p$ fulfils an inequality. The goal of the paper is to show that, in the case of the opposite inequality for $p$, all solutions of the equation considered are oscillating for $n$ tending to $\infty$.

Keywords

Discrete delayed equation, oscillating solution, positive solution, asymptotic behavior.

RIV year

2011

Released

24.10.2011

Publisher

EPI

Location

Kunovice

ISBN

978-80-7314-221-6

Book

NINTH INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS, ICSC 2011

Pages from

95

Pages to

101

Pages count

7

BibTex

```
@inproceedings{BUT74172,
author="Josef {Diblík} and Alena {Baštincová} and Jaromír {Baštinec}",
title="Oscillation of solution of a linear third-order discrete delayed equation",
annote="A linear third-order discrete delayed equation $Delta x(n)=-p(n)x(n-2)$ with a positive coefficient $p$ is considered for $n$ going to $\infty$. This equation is known to have a positive solution if $p$ fulfils an inequality. The goal of the paper is to show that, in the case of the opposite inequality for $p$, all solutions of the equation considered are oscillating for $n$ tending to $\infty$.",
address="EPI",
booktitle="NINTH INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS, ICSC 2011",
chapter="74172",
howpublished="print",
institution="EPI",
year="2011",
month="october",
pages="95--101",
publisher="EPI",
type="conference paper"
}
```