On the dynamics of the difference equation xn+1=1Bnxn+xn-1

摘要

In this note we study the following non-autonomous equation:xn+1=1Bnxn+xn-1,n=0,1,…,where Bn>0 is a period-2 sequence and the initial values x-1,x0∈(0,+∞). We show that the unique prime period-2 solution of this equation is globally asymptotically stable, which answer Open Problem 5 proposed by Camouzis and Ladas [6].