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

Authors: R. DeVault, G. Ladas and S. W. Schultz
Journal: Proc. Amer. Math. Soc. 126 (1998), 3257-3261
MSC (1991): Primary 39A10
MathSciNet review: 1473661
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Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [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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Additional Information

R. DeVault
Affiliation: Division of Mathematics and Sciences, Northwestern State University, Natchitoches, Louisiana 71497

G. Ladas
Affiliation: Department of Mathematics, University of Rhode Island, Kingston, Rhode Island 02881

S. W. Schultz
Affiliation: Department of Mathematics and Computer Science, Providence College, Providence, Rhode Island 02918

Keywords: Recursive sequence, global asymptotic stability, period two solution
Received by editor(s): March 18, 1997
Communicated by: Hal L. Smith
Article copyright: © Copyright 1998 American Mathematical Society