## On the recursive sequence $$x_{n+1}=\frac{\alpha+\beta x_{n-1}}{\gamma+x_n}$$.(English)Zbl 1039.39004

Summary: We investigate the boundedness character, the oscillatory and periodic nature, and the global stability behavior of the nonnegative solutions of the difference equation $x_{n+1}= \frac {\alpha+\beta x_{n-1}} {\gamma+x_n},\;n=0,1,\dots$ where the parameters $$\alpha,\beta$$, and $$\gamma$$ are nonnegative real numbers.

### MSC:

 39A11 Stability of difference equations (MSC2000) 39A20 Multiplicative and other generalized difference equations