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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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 , , 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.

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

First available in Project Euclid: 1 November 2010

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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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