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Zbl 1039.39004
Gibbons, C. H.; Kulenovic, M. R. S.; Ladas, G.
On the recursive sequence $x_{n+1}=\frac{\alpha+\beta x_{n-1}}{\gamma+x_n}$. (English)
[J] Math. Sci. Res. Hot-Line 4, No. 2, 1-11 (2000). ISSN 1087-9919

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 2000:: *39A11 Stability of difference equations
39A20 Generalized difference equations

Keywords: bounded solution; multiplicative difference equation; oscillation; period-two solution; global stability; nonnegative solutions

Cited in: Zbl 1203.39010 Zbl 1100.39001

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