On the recursive sequence x n+1 = α n + x n-1 /x n II

Abstract

In this paper we investigate the boundedness character and the periodic nature of the positive solutions of the difference equation X n+i = α n + x n-1 /x n , n = 0,1,2,..., where α n is a two periodic sequence of nonnegative real numbers and where the initial conditions x -1 and x 0 are arbitrary positive real numbers.