Publication detail

# A final result on the oscillation of solutions of the linear discrete delayed equation \Delta x(n)=-p(n)x(n-k) with a positive coefficient

BAŠTINEC, J. BEREZANSKY, L. DIBLÍK, J. ŠMARDA, Z.

Original Title

A final result on the oscillation of solutions of the linear discrete delayed equation \Delta x(n)=-p(n)x(n-k) with a positive coefficient

English Title

A final result on the oscillation of solutions of the linear discrete delayed equation \Delta x(n)=-p(n)x(n-k) with a positive coefficient

Type

journal article - other

Language

en

Original Abstract

A linear $(k+1)$th-order discrete delayed equation $\Delta x(n)=-p(n)x(n-k)$ where $p(n)$ is a positive sequence is considered for $n\to\infty$. This equation is known to have a positive solution if the sequence $p(n)$ satisfies an inequality. Our aim is to show that, in the case of the opposite inequality for $p(n)$, all solutions of the equation considered are oscillating for $n\to\infty$.

English abstract

A linear $(k+1)$th-order discrete delayed equation $\Delta x(n)=-p(n)x(n-k)$ where $p(n)$ is a positive sequence is considered for $n\to\infty$. This equation is known to have a positive solution if the sequence $p(n)$ satisfies an inequality. Our aim is to show that, in the case of the opposite inequality for $p(n)$, all solutions of the equation considered are oscillating for $n\to\infty$.

Keywords

linear discrete delayed equation, positive sequence, positive solution, opposite inequality, oscillating solution,

RIV year

2011

Released

08.08.2011

ISBN

1085-3375

Periodical

Abstract and Applied Analysis

Year of study

vol. 2011,

Number

Article ID 58632

State

US

Pages from

1

Pages to

28

Pages count

28

Documents

BibTex

```
@article{BUT73392,
author="Jaromír {Baštinec} and Leonid {Berezansky} and Josef {Diblík} and Zdeněk {Šmarda}",
title="A final result on the oscillation of solutions of the linear discrete delayed equation \Delta x(n)=-p(n)x(n-k) with a positive coefficient",
annote="A linear $(k+1)$th-order discrete delayed equation $\Delta x(n)=-p(n)x(n-k)$ where $p(n)$ is a positive sequence is considered for $n\to\infty$. This equation is known to have a positive solution if the sequence $p(n)$ satisfies an inequality. Our aim is to show that, in the case of the opposite inequality for $p(n)$, all solutions of the equation considered are oscillating for $n\to\infty$.",
chapter="73392",
number="Article ID 58632",
volume="vol. 2011,",
year="2011",
month="august",
pages="1--28",
type="journal article - other"
}
```