Copyright © 2010 Xiu-Mei Jia et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The main goal of the paper is to investigate boundedness, invariant intervals, semicycles, and global attractivity of all nonnegative solutions of the equation xn+1=(α+βxn+γxn-k)/(1+xn-k), n∈ℕ0, where the parameters α,β,γ∈[0,∞), k≥2 is an integer, and the initial conditions x-k,…,x0∈[0,∞). It is shown that the unique positive equilibrium of the equation is globally asymptotically stable under the condition β≤1. The result partially solves the open problem proposed by Kulenović and Ladas in work (2002).