Detail publikace

# Asymptotic behavior of positive solutions of a discrete delayed equation

Originální název

Asymptotic behavior of positive solutions of a discrete delayed equation

Anglický název

Asymptotic behavior of positive solutions of a discrete delayed equation

Jazyk

en

Originální abstrakt

Denote ${\Z}_s^q:=\{s,s+1,\dots,q\}$ where $s$ and $q$ are integers such that $s\leq q$. Similarly a set ${\Z}_s^{\infty}$ is defined. In the paper the scalar discrete equation with delay \begin{equation} \Delta x(n)=-\left(\frac{k}{k+1}\right)^k \frac{1}{k+1} \left[1+\omega(n)\right] x(n-k) \end{equation} is considered where function $\omega \colon {\Z}_a^{\infty}\to\R$ has a special form, $k\ge1$ is fixed integer, $n\in {\Z}_a^{\infty}$, and $a$ is a whole number. We prove that there exists a positive solution $x=x(n)$ of the equation and give its upper estimation.

Anglický abstrakt

Denote ${\Z}_s^q:=\{s,s+1,\dots,q\}$ where $s$ and $q$ are integers such that $s\leq q$. Similarly a set ${\Z}_s^{\infty}$ is defined. In the paper the scalar discrete equation with delay \begin{equation} \Delta x(n)=-\left(\frac{k}{k+1}\right)^k \frac{1}{k+1} \left[1+\omega(n)\right] x(n-k) \end{equation} is considered where function $\omega \colon {\Z}_a^{\infty}\to\R$ has a special form, $k\ge1$ is fixed integer, $n\in {\Z}_a^{\infty}$, and $a$ is a whole number. We prove that there exists a positive solution $x=x(n)$ of the equation and give its upper estimation.

BibTex


@inproceedings{BUT133458,
author="Jaromír {Baštinec} and Josef {Diblík}",
title="Asymptotic behavior of positive solutions of a discrete delayed equation",
annote="Denote ${\Z}_s^q:=\{s,s+1,\dots,q\}$ where $s$ and $q$ are integers
such that $s\leq q$. Similarly a set ${\Z}_s^{\infty}$ is defined.
In the paper the scalar discrete equation with delay
\begin{equation}
\Delta x(n)=-\left(\frac{k}{k+1}\right)^k \frac{1}{k+1}
\left[1+\omega(n)\right] x(n-k)
\end{equation}
is considered where function $\omega \colon {\Z}_a^{\infty}\to\R$
has a special form, $k\ge1$ is fixed integer,
$n\in {\Z}_a^{\infty}$, and $a$ is a whole number. We prove that
there exists a positive  solution $x=x(n)$ of the
equation  and give its upper estimation.",
}