Publication result 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

Peer-reviewed article not indexed in WoS or Scopus

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,

Key words in English

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

Authors

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

RIV year

2012

Released

08.08.2011

ISBN

1085-3375

Periodical

Abstract and Applied Analysis

Volume

vol. 2011,

Number

Article ID 58632

State

United States of America

Pages from

1

Pages to

28

Pages count

28

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",
  journal="Abstract and Applied Analysis",
  year="2011",
  volume="vol. 2011,",
  number="Article ID 58632",
  pages="1--28",
  issn="1085-3375"
}