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

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)].


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


Zbl 0993.39008
Full Text: DOI


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