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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
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