Periodic solutions to a third-order conditional difference equation over the integers
type: Item
instance of: scholarly article
title: Periodic solutions to a third-order conditional difference equation over the integers
zbMATH Open document ID: 1232.39016
DOI: 10.1155/2011/827235
author: Li He
author: Wanping Liu
published in: Discrete Dynamics in Nature and Society
publication date: 2012-01-23T00:00:00Z
review text: Summary: We study a third-order conditional difference equation which is a generalization from the literature. We investigate this equation by transforming it into a first-order system. Finally it is proved that the equation has no period-two (or three) integer solutions. Besides, its all period-four (and five) integer solutions are derived under appropriate rational parameters.
Mathematics Subject Classification ID: 39A23
Mathematics Subject Classification ID: 39A10
zbMATH DE Number: 5999659
zbMATH Keywords: third-order conditional difference equation
zbMATH Keywords: first-order system
Wikidata QID: Q58655546
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2011/827235
OpenAlex ID: W2140497781
cites work: Editorial: Abstract differential and difference equations
cites work: On some difference equations with eventually periodic solutions
cites work: Periodic solutions of arbitrary length in a simple integer iteration
cites work: On the eventual periodicity of with a period-four parameter
cites work: Periodic solutions to some difference equations over the integers
cites work: Open problems and conjectures
cites work: Quantitative bounds for positive solutions of a Stević difference equation
cites work: On some \(k\)-dimensional cyclic systems of difference equations
cites work: On global attractivity of a class of nonautonomous difference equations
cites work: Global behavior of two families of nonlinear symmetric difference equations
cites work: Part-metric and its applications to cyclic discrete dynamic systems
cites work: Boundedness character of a class of difference equations
cites work: Boundedness character of a fourth order nonlinear difference equation
cites work: On the periodicity of the sequence
cites work: On the recursive sequence \(x_{n+1} = \max \left\{ c, \frac {x_n^p}{x_{n-1}^p} \right\}\)
cites work: Global stability of a difference equation with maximum
cites work: Global stability of a max-type difference equation
cites work: On a generalized max-type difference equation from automatic control theory
cites work: On a max-type difference inequality and its applications
cites work: On a nonlinear generalized max-type difference equation
cites work: Global attractivity of a family of max-type difference equations
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description: scientific article; zbMATH DE number 5999659