On the solutions of a second order difference equation

R. Abo-Zeid

In this paper, we discuss the global behavior of all solutions of the difference equation $x_{n+1} = \frac{x_{n}x_{n-1}}{ax_{n} + bx_{n-1}},\quad n\in\mathbb{N}_{0},$ where $a,b$ are real numbers and the initial conditions $x_{-1},x_{0}$ are real numbers. We determine the forbidden set and give an explicit formula for the solutions. We show the existence of periodic solutions, under certain conditions.