Mathematica Eterna
Open Access

Abstract

Global Behavior of a Higher Order Nonlinear Difference Equation

Guomei Tang, Hua Liu

In this paper, we consider the higher order nonlinear rational difference equation xn+1 = α + xn + γxn−k A + xn−k , n = 0, 1, · · · with the parameters and the initial conditions x−k, · · · , x0 are nonnegative real numbers. We investigate the periodic character, invariant intervals and the global asymptotic stability of all positive solutions of the above mentioned equation. In particular, our results partially confirm the conjecture introduced by Amleh and Ladas in their paper.