On the rational (k + 1, k + 1)-type difference equation

Abstract

In this paper we investigate the boundedness character of the positive solutions of the rational difference equation of the form xn+1 = a 0 + ∑ j=1k a jx n-j+1/b 0 + ∑ j=1k a jx n-j+1. n= 0,1,... where k ∈ N, and a j, b j, j = 0, 1,... ,k, are nonnegative numbers such that b 0 + + ∑ j=1k a jx n-j+1 > 0 for every n ∈ N∪{0}. In passing we confirm several conjectures recently posed in the paper: E. Camouzis, G. Ladas and E. P. Quinn, On third order rational difference equations (part 6), J. Differ. Equations Appl. 11(8) (2005), 759-777.