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On the oscillation and periodic character of a third order rational difference equation

Authors:	W T Patula H D Voulov

Institution:	Department of Mathematics, Southern Illinois University Carbondale, Carbondale, Illinois 62901-4408 ; Department of Mathematics, Southern Illinois University Carbondale, Carbondale, Illinois 62901-4408

Abstract:	We prove that every positive solution of the following difference equation: $\begin{displaymath}x_n = 1 + \frac{x_{n-2}}{x_{n-3}}, \quad n = 0,1,\ldots, \end{displaymath}$ converges to a period two solution.

Keywords:	Periodic solution semicycles oscillation

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