## Abstract and Applied Analysis

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

#### 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