Publication detail

# Positive solutions of nonlinear discrete equations

BAŠTINEC, J. DIBLÍK, J. HALFAROVÁ, H.

Original Title

Positive solutions of nonlinear discrete equations

English Title

Positive solutions of nonlinear discrete equations

Type

conference paper

Language

en

Original Abstract

A delayed discrete equation $\Delta x(n)=f(n,x(n),x(n-1),\dots,x(n-k))$ is considered where $n=a+k,a+k+1,\dots$ and $a\in\mathbb{N}$. It is proved that, given some conditions for $f,$ there exists a positive solution $x=x(n)$ for $n\to \infty$. The rate of convergence of a positive solution is estimated as well.

English abstract

A delayed discrete equation $\Delta x(n)=f(n,x(n),x(n-1),\dots,x(n-k))$ is considered where $n=a+k,a+k+1,\dots$ and $a\in\mathbb{N}$. It is proved that, given some conditions for $f,$ there exists a positive solution $x=x(n)$ for $n\to \infty$. The rate of convergence of a positive solution is estimated as well.

Keywords

Discrete equation, delayed equation, asymptotic decomposition, positive solution.

Released

05.02.2019

Publisher

Slovak University of Technology

Location

Bratislava

ISBN

978-80-227-4884-1

Book

18th conference on aplied mathematics. Aplimat 2019 Proceedings.

Edition number

1

Pages from

23

Pages to

30

Pages count

8

Documents

BibTex


@inproceedings{BUT157460,
author="Jaromír {Baštinec} and Josef {Diblík} and Hana {Halfarová}",
title="Positive solutions of nonlinear discrete equations",
annote="A delayed discrete equation  $\Delta x(n)=f(n,x(n),x(n-1),\dots,x(n-k))$  is considered where $n=a+k,a+k+1,\dots$ and $a\in\mathbb{N}$. It is proved that, given some conditions for $f,$ there exists a positive solution $x=x(n)$ for $n\to \infty$. The rate of convergence of a positive solution is estimated as well.
",
}