Abstract and Applied Analysis

Solutions of the Difference Equation ${x}_{n+1}={x}_{n}{x}_{n-1}-1$

Candace M. Kent, Witold Kosmala, Michael A. Radin, and Stevo Stević

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Abstract

Our goal in this paper is to investigate the long-term behavior of solutions of the following difference equation: ${x}_{n+1}={x}_{n}{x}_{n-1}-1$, $n=0,1,2,\ldots ,$ where the initial conditions ${x}_{-1}$ and ${x}_{0}$ are real numbers. We examine the boundedness of solutions, periodicity of solutions, and existence of unbounded solutions and how these behaviors depend on initial conditions.

Article information

Source
Abstr. Appl. Anal. Volume 2010 (2010), Article ID 469683, 13 pages.

Dates
First available in Project Euclid: 1 November 2010

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1288620747

Digital Object Identifier
doi:10.1155/2010/469683

Mathematical Reviews number (MathSciNet)
MR2672190

Zentralblatt MATH identifier
1198.39017

Citation

Kent, Candace M.; Kosmala, Witold; Radin, Michael A.; Stević, Stevo. Solutions of the Difference Equation x n + 1 = x n x n − 1 − 1 . Abstr. Appl. Anal. 2010 (2010), Article ID 469683, 13 pages. doi:10.1155/2010/469683. https://projecteuclid.org/euclid.aaa/1288620747


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