On a Max-Type Difference Equation

Abstract

We study the behaviour of the solutions of the following difference equation with the max operator: xn+1=max{1/xn,Axn−1}, n∈ℕ0, where parameter A∈ℝ and initial values x−1 and x0 are nonzero real numbers. In the most of the cases we determine the behaviour of the solutions in the terms of the initial values x−1 and x0 and the parameter A.