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BAŠTINEC, J. DIBLÍK, J.
Original Title
Asymptotic behavior of positive solutions of a discrete delayed equation
Type
conference paper
Language
English
Original Abstract
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.
Keywords
discrete equation with delay, positive solution,upper estimation
Authors
BAŠTINEC, J.; DIBLÍK, J.
Released
31. 1. 2017
Publisher
STU Bratislava
Location
Bratislava
ISBN
978-80-227-4650-2
Book
Aplimat 2017, proceedings
Edition number
1
Pages from
63
Pages to
68
Pages count
6
BibTex
@inproceedings{BUT133458, author="Jaromír {Baštinec} and Josef {Diblík}", title="Asymptotic behavior of positive solutions of a discrete delayed equation", booktitle="Aplimat 2017, proceedings", year="2017", number="1", pages="63--68", publisher="STU Bratislava", address="Bratislava", isbn="978-80-227-4650-2" }