Detail publikace

# Weighted asymptotically periodic solutions of linear volterra difference equations

Originální název

Weighted asymptotically periodic solutions of linear volterra difference equations

Anglický název

Weighted asymptotically periodic solutions of linear volterra difference equations

Jazyk

en

Originální abstrakt

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.

Anglický abstrakt

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.

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"
}