Authors: Berenhaut, Kenneth
Foley, John
Stević, Stevo 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Boundedness character of positive solutions of a max difference equation
Journal: Journal of Difference Equations and Applications
Volume: 12
Issue: 12
First page: 1193
Last page: 1199
Issue Date: 1-Dec-2006
Rank: M21
ISSN: 1023-6198
DOI: 10.1080/10236190600949766
Abstract: 
This paper studies the boundedness character of the positive solutions of the difference equation. where k, m ε ℕ with gcd(k, m)=1. We prove that if c ≥ 1, then every solution of the equation is bounded, and if c ε (0, 1) and k is even, then there exist positive unbounded solutions. For the case c ε(0, 1) and k odd, we consider the related equation yn = max{-1, yn-k - yn-m} and show that every integer solution is eventually periodic.
Keywords: Boundedness | Max difference equation | Periodic solution | Positive solution
Publisher: Taylor & Francis

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