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A trichotomy result for non-autonomous rational difference equations

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Palladino F., Radin M.

Open Mathematics

2011

tom 9

nr 5

1135-1142

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.

Unbounded solutions of the max-type difference equation $$ x_{n + 1} = max\left\{ {\frac{{A_n }} {{X_n }},\frac{{B_n }} {{X_{n - 2} }}} \right\} $$

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Kerbert C., Radin M.

Open Mathematics

2008

tom 6

nr 2

307-324

We investigate the boundedness nature of positive solutions of the difference equation $$ x_{n + 1} = max\left\{ {\frac{{A_n }} {{X_n }},\frac{{B_n }} {{X_{n - 2} }}} \right\},n = 0,1,..., $$ where {A n}n=0∞ and {B n}n=0∞ are periodic sequences of positive real numbers.

Ograniczanie wyników

2 Open Mathematics

2 Radin M.

1 Kerbert C.

1 Palladino F.

1 2011

1 2008

Wyniki wyszukiwania

A trichotomy result for non-autonomous rational difference equations

Unbounded solutions of the max-type difference equation $$ x_{n + 1} = max\left\{ {\frac{{A_n }} {{X_n }},\frac{{B_n }} {{X_{n - 2} }}} \right\} $$