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Zbl 1100.39014
Stević, Stevo
On the recursive sequence $x_{n+1}=\frac{\alpha+\beta x_{n-k}}{f(x_n,\dots,x_{n-k+1})}$.
(English)
[J] Taiwanese J. Math. 9, No. 4, 583-593 (2005). ISSN 1027-5487

The paper discusses qualitative properties for the solutions of the difference equation $$x_{n+1}= {{(\alpha+\beta x_{n-k})}\over{f(x_n,\ldots,x_{n-k+1})}}$$ with $\alpha\geq 0\;,\;\beta\geq 0$ and $f:\Bbb R_+^k\to\Bbb R_+$ continuous and non-decreasing in each argument such that $f(0,0,\ldots,0)>0$. Only nonnegative solutions are considered. Several cases are tackled: $\beta<1$; $\beta>1$; $\beta=1, \alpha>0$. An open problem is finally stated.
MSC 2000:
*39A11 Stability of difference equations
39A20 Generalized difference equations

Keywords: rational difference equation; positive solution; oscillation; boundedness; stability

Cited in: Zbl 1203.39010

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