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Unbounded solutions of the max-type difference equation $x_{n + 1} = m a x \{\frac{A_{n}}{X_{n}}, \frac{B_{n}}{X_{n - 2}}\}$

Christopher Kerbert; Michael Radin — 2008

Open Mathematics

We investigate the boundedness nature of positive solutions of the difference equation $x_{n + 1} = m a x \{\frac{A_{n}}{X_{n}}, \frac{B_{n}}{X_{n - 2}}\}, n = 0, 1, . . .,$ where A nn=0∞ and B nn=0∞ are periodic sequences of positive real numbers.

A trichotomy result for non-autonomous rational difference equations

Frank Palladino; Michael Radin — 2011

Open Mathematics

We study non-autonomous rational difference equations. Under the assumption of a periodic non-autonomous parameter, we show that a well known trichotomy result in the autonomous case is preserved in a certain sense which is made precise in the body of the text. In addition we discuss some questions regarding whether periodicity preserves or destroys boundedness.

Solutions of the difference equation $x_{n + 1} = x_{n} x_{n - 1} - 1$ .

Kent, Candace M.; Kosmala, Witold; Radin, Michael A.; Stević, Stevo — 2010

Abstract and Applied Analysis

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