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

Authors:
R. DeVault, G. Ladas and S. W. Schultz

Journal:
Proc. Amer. Math. Soc. **126** (1998), 3257-3261

MSC (1991):
Primary 39A10

DOI:
https://doi.org/10.1090/S0002-9939-98-04626-7

MathSciNet review:
1473661

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Abstract | References | Similar Articles | Additional Information

Abstract: We show that every positive solution of the equation \[ x_{n+1} = \frac {A}{x_{n}} + \frac {1}{x_{n-2}}, \hspace {.2in} n = 0, 1, \ldots , \] where $A \in (0, \infty )$, converges to a period two solution.

- G. Ladas, Open Problems and Conjectures, Journal of Difference Equations and Applications 2 (1996), 449-452.
- Ch. G. Philos, I. K. Purnaras, and Y. G. Sficas,
*Global attractivity in a nonlinear difference equation*, Appl. Math. Comput.**62**(1994), no. 2-3, 249–258. MR**1284547**, DOI https://doi.org/10.1016/0096-3003%2894%2990086-8

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Additional Information

**R. DeVault**

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

Email:
rich@alpha.nsula.edu

**G. Ladas**

Affiliation:
Department of Mathematics, University of Rhode Island, Kingston, Rhode Island 02881

Email:
gladas@math.uri.edu

**S. W. Schultz**

Affiliation:
Department of Mathematics and Computer Science, Providence College, Providence, Rhode Island 02918

Email:
sschultz@providence.edu

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