On the global character of the difference equation x(n+1)=(alpha)+(gamma)xn-(2k+1)+(delta)xn-2|A+xn-2|

Abstract

We investigate the global stability, the periodic character, and the boundedness nature of solutions of the difference equation x(n+1)=(alpha)+(gamma)xn-(2k+1)+(delta)xn-2|A+xn-2|, n=0,1,... where k and l are non-negative integers, the parameters (alpha), (gamma), (delta), A are non-negative real numbers with (alpha)+(gamma)+(delta)>0, and the initial conditions are non-negative real numbers. We show that the solutions exhibit a trichotomy character depending upon the parameters (gamma), (delta) and A (Refer to PDF file for exact formulas).