### On a fourth order rational difference equation

#### R. Abo-Zeid

In this paper, we determine and study the behavior of all admissible solutions of the difference equation $$x_{n+1}=\frac{x_{n}x_{n-2}}{ax_{n-2}+ bx_{n-3}},\quad n=0,1,\ldots,$$ where $a,b$ are positive real numbers and the initial conditions $x_{-3}, x_{-2}, x_{-1}, x_0$ are real numbers. We show when $a=b=1$ that, every admissible solution converges to $0$.

Tbilisi Mathematical Journal, Vol. 12(4) (2019), pp. 71-79