Amleh, A. M.; Grove, E. A.; Ladas, G.; Georgiou, D. A. On the recursive sequence \(x_{n+1}=\alpha+x_{n-1}/x_n\). (English) Zbl 0962.39004 J. Math. Anal. Appl. 233, No. 2, 790-798 (1999). 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. Cited in 3 ReviewsCited in 148 Documents MSC: 39A11 Stability of difference equations (MSC2000) Keywords:period-2 solutions; global stability; boundedness; positive solutions; difference equation PDF BibTeX XML Cite \textit{A. M. Amleh} et al., J. Math. Anal. Appl. 233, No. 2, 790--798 (1999; Zbl 0962.39004) Full Text: DOI OpenURL References: [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 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.