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On the recursive sequence \(x_{n+1}=\alpha+x_{n-1}/x_n\). (English) Zbl 0962.39004

Summary: We study the global stability, the boundedness character, and the periodic nature of the positive solutions of the difference equation \(x_{n+1}= \alpha+ x_{n-1}/x_n\), where \(\alpha \in[0, \infty)\), and where the initial conditions \(x_{-1}\) and \(x_0\) are arbitrary positive real numbers.

MSC:

39A11 Stability of difference equations (MSC2000)
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References:

[1] Kocic, V.L.; Ladas, G., Global behavior of nonlinear difference equations of higher order with applications, (1993), Kluwer Academic Publishers Dordrecht · Zbl 0787.39001
[2] Kulenović, M.R.S.; Ladas, G.; Sizer, W.S., On the recursive sequencexn=(αxn+βxn)/(γxn+δxn), Math. sci. res. hot-line, 2, 1-16, (1998) · Zbl 0960.39502
[3] G. Ladas, Open problems and conjectures, J. Differential Equations Appl. 5 · Zbl 1057.39505
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