On the Recursive Sequence xn+1=A+(xn−1p/xnq)

Abstract

In this paper we study the boundedness, the persistence, the attractivity and the stability of the positive solutions of the nonlinear difference equation xn+1=α+(xn−1p/xnq), n=0,1,…, where α,p,q∈(0,∞) and x−1,x0∈(0,∞). Moreover we investigate the existence of a prime two periodic solution of the above equation and we find solutions which converge to this periodic solution.