## 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)
Full Text:

### 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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.