Invariants for some difference equations
type: Item
instance of: scholarly article
title: Invariants for some difference equations
zbMATH Open document ID: 0879.39001
published in: Journal of Mathematical Analysis and Applications
publication date: 1998-01-18T00:00:00Z
review text: A function \(I(x_{n-k},\dots, x_n)\) is called an invariant of the difference equation \(x_{n+1}= f(x_n,\dots,\) \(x_{n-k})\), if \(I\) is constant for every solution \(x_n\) and for all \(n\geq 0\). A positive solution is said to persist if it is bounded away from zero. For three types of nonlinear difference equations, invariants are constructed, and the invariants are used to see whether all solutions are bounded and persist. Analogous considerations are made for three systems of difference equations.
Mathematics Subject Classification ID: 39A10
zbMATH DE Number: 1053564
zbMATH Keywords: persistence
zbMATH Keywords: bounded solution
zbMATH Keywords: positive solution
zbMATH Keywords: nonlinear difference equations
zbMATH Keywords: invariants
zbMATH Keywords: systems
author: C. J. Schinas
reviewed by: Lothar Berg
MaRDI profile type: Publication
OpenAlex ID: W2038600925
cites work: Q3837530
cites work: Q4381451
cites work: Q5688579
cites work: Open problems and conjectures
cites work: On may's host parasitoid model
DOI: 10.1006/JMAA.1997.5499
description: scientific article; zbMATH DE number 1053564