Publication detail

# Weighted asymptotically periodic solutions of linear volterra difference equations

DIBLÍK, J. RŮŽIČKOVÁ, M. SCHMEIDEL, E. ZBASZYNIAK, M.

Original Title

Weighted asymptotically periodic solutions of linear volterra difference equations

English Title

Weighted asymptotically periodic solutions of linear volterra difference equations

Type

journal article - other

Language

en

Original Abstract

A linear Volterra difference equation of the form $$x(n+1)=a(n)+b(n)x(n)+\sum\limits^{n}_{i=0}K(n,i)x(i)$$ where $x\colon\bN_0\to\bR$, $a\colon \bN_0\to\bR$, $K\colon\bN_0\times\bN_0\to \bR$ and $b\colon\bN_0 \to \bR\setminus\{0\}$ is $\omega$-periodic is considered. Sufficient conditions for the existence of weighted asymptotically periodic solutions of this equation are obtained. Unlike previous investigations, no restriction on $\prod_{j=0}^{\omega-1}b(j)$ is assumed. The results generalize some of the recent results.

English abstract

A linear Volterra difference equation of the form $$x(n+1)=a(n)+b(n)x(n)+\sum\limits^{n}_{i=0}K(n,i)x(i)$$ where $x\colon\bN_0\to\bR$, $a\colon \bN_0\to\bR$, $K\colon\bN_0\times\bN_0\to \bR$ and $b\colon\bN_0 \to \bR\setminus\{0\}$ is $\omega$-periodic is considered. Sufficient conditions for the existence of weighted asymptotically periodic solutions of this equation are obtained. Unlike previous investigations, no restriction on $\prod_{j=0}^{\omega-1}b(j)$ is assumed. The results generalize some of the recent results.

Keywords

Linear Volterra difference equation, weighted asymptotically periodic solution

RIV year

2011

Released

03.08.2011

ISBN

1085-3375

Periodical

Abstract and Applied Analysis

Year of study

2011

Number

1

State

US

Pages from

1

Pages to

14

Pages count

14

Documents

BibTex


@article{BUT72873,
author="Josef {Diblík} and Miroslava {Růžičková} and Ewa {Schmeidel} and Malgorzata {Zbaszyniak}",
title="Weighted asymptotically periodic solutions of linear volterra difference equations",
annote="A linear Volterra difference equation of the form
$$x(n+1)=a(n)+b(n)x(n)+\sum\limits^{n}_{i=0}K(n,i)x(i)$$
where $x\colon\bN_0\to\bR$,
$a\colon \bN_0\to\bR$, $K\colon\bN_0\times\bN_0\to \bR$ and
$b\colon\bN_0 \to \bR\setminus\{0\}$ is
$\omega$-periodic is considered.
Sufficient conditions for the existence
of weighted asymptotically  periodic solutions of this equation are obtained.
Unlike previous investigations,
no restriction on $\prod_{j=0}^{\omega-1}b(j)$ is assumed.
The results generalize some of the recent results.",
chapter="72873",
number="1",
volume="2011",
year="2011",
month="august",
pages="1--14",
type="journal article - other"
}