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On the recursive sequence ${\displaystyle}x_{n+1}=\frac A{x_n}+\frac 1{x_{n-2}}$

Author(s): R. DeVault; G. Ladas; S. W. Schultz
Journal: Proc. Amer. Math. Soc. 126 (1998), 3257-3261.
MSC (1991): Primary 39A10
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Abstract: We show that every positive solution of the equation

$\begin{displaymath}x_{n+1} = \frac{A}{x_{n}} + \frac{1}{x_{n-2}}, \hspace{.2in} n = 0, 1, \ldots , \end{displaymath}$

where $A \in (0, \infty)$ , converges to a period two solution.

References:

[1]: G. Ladas, Open Problems and Conjectures, Journal of Difference Equations and Applications 2 (1996), 449-452.
[2]: Ch. G. Philos, I. K. Purnaras and Y. G. Sficas, Global attractivity in a nonlinear difference equation, Applied Mathematics and Computers 62, (1994), 249 - 258. MR 95h:39008


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