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.


39A11 Stability of difference equations (MSC2000)
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[1] Kocic, V. L.; Ladas, G., Global Behavior of Nonlinear Difference Equations of Higher Order with Applications (1993), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht · Zbl 0787.39001
[2] Kulenović, M. R.S.; Ladas, G.; Sizer, W. S., On the recursive sequence \(x_n\)=(α\(x_n\)+β \(x_n )\)/(γ\(x_n\)+δ \(x_n )\), Math. Sci. Res. Hot-line, 2, 1-16 (1998) · Zbl 0960.39502
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