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Zbl 0985.39017
Kulenović, M.R.S.; Ladas, G.; Prokup, N.R.
A rational difference equation. (English)
[J] Comput. Math. Appl. 41, No.5-6, 671-678 (2001). ISSN 0898-1221

The authors investigate the nonlinear rational difference equation $$x_{n+1}= (\alpha x_n+ \beta x_{n-1})/(A+x_{n-1}),\ n=0,1,2,\dots, \tag *$$ where the parameters $\alpha,\beta$ and $A$ and the initial conditions $x_{-1}$ and $x_0$ are nonnegative real numbers. The Riccati difference equation and the Pielou discrete delay logistic model are obtained from (*) for $\alpha=0$ and $\beta=0$, respectively. The boundedness character, the periodic nature, and the global asymptotic stability of all positive solutions of the equation (*) with $\alpha> 0$, $\beta>0$, $A\ge 0$, are studied.
[Pavel Talpalaru (Iaşi)]

MSC 2000:: *39B05 General theory of functional equations
39A11 Stability of difference equations

Keywords: bounded solutions; periodic solutions; nonlinear rational difference equation; Riccati difference equation; Pielou discrete delay logistic model; asymptotic stability; positive solutions

Cited in: Zbl 1185.37025 Zbl 1055.39028

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