On boundedness of the solutions of the difference equation xn+1=xn−1/(p+xn)

Abstract

We study the difference equation xn+1=xn−1/(p+xn), n=0,1,…, where initial values x−1,x0∈(0,+∞) and 0<p<1, and obtain the set of all initial values (x−1,x0)∈(0,+∞)×(0,+∞) such that the positive solution {xn}n=−1∞ is bounded. This answers the Open Problem 2 proposed by Kulenović and Ladas.