Boundedness character of positive solutions of a max difference equation

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.