On the Global Attractivity of a Max-Type Difference Equation

Abstract

We investigate asymptotic behavior and periodic nature of positive solutions of the difference equation 𝑥𝑛=max{𝐴/𝑥𝑛−1,1/𝑥𝛼𝑛−3},𝑛=0,1,…, where 𝐴>0 and 0<𝛼<1. We prove that every positive solution of this difference equation approaches 𝑥=1 or is eventually periodic with period 2.