On the oscillation and periodic character of a third order rational difference equation. (English) Zbl 1014.39010

Patula, W. T.; Voulov, H. D.

Proc. Am. Math. Soc. 131, No. 3, 905-909 (2003).

The authors prove that every positive solution of the following difference equation \[ x_n=1+{x_{n-2}\over x_{n-3}},\;n=0,1,\dots, \] converges to a periodic solution. As to some related results, see El-Metwally, E. A. Grove, G. Ladas and H. D. Voulov [J. Difference Equ. Appl. 7, No. 6, 837-850 (2001; Zbl 0993.39008)].

Reviewer: Mingshu Peng (Beijing)

MSC:

39A11	Stability of difference equations (MSC2000)
39B05	General theory of functional equations and inequalities

Keywords:

third order rational difference equation; periodic solution; semicycles; oscillation; positive solution

Citations:

Zbl 0993.39008

References:

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