Solutions of the Difference Equation 𠑥 𠑛 + 1 = 𠑥 𠑛 𠑥 𠑛 − 1 − 1

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

Abstract and Applied Analysis, 2010, vol. 2010, 1-13

Abstract:

Our goal in this paper is to investigate the long-term behavior of solutions of the following difference equation: 𠑥 𠑛 + 1 = 𠑥 𠑛 𠑥 𠑛 − 1 − 1 , 𠑛 = 0 , 1 , 2 , … , where the initial conditions 𠑥 − 1 and 𠑥 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.

Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:469683

DOI: 10.1155/2010/469683

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