### Global Behavior of a Fourth Order Rational Difference Equation

#### Abstract

In this paper, we investigate the global stability, periodic nature, and the oscillation of solutions of the difference equation \[x_{n+1}=\frac{Ax_{n-3}}{B+Cx_{n-2}^{2}},\qquad n=0,1,2,\ldots\] where $A,C,B>0$ and the initial conditions $x_{-3},x_{-2},x_{-1},x_0$ are nonnegative real numbers. We show that under certain conditions unbounded solutions will be obtained.

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