On the Solutions of a Third Order Rational Difference Equation

Raafat Abo-Zeid, Hossam Kamal

Abstract

In this paper, we discuss the global behavior of all admissible solutions of the difference equation

$$x_{n+1}=\frac{Ax_{n-2}}{B- Cx_{n}x_{n-1}x_{n-2}},\quad n=0,1,\ldots, $$

where  $A,B,C$  are positive real numbers  and the initial conditions $x_{-2},x_{-1},x_0$ are real numbers.