On a fifth-order difference equation (Q2792465)
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scientific article; zbMATH DE number 6554660
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a fifth-order difference equation |
scientific article; zbMATH DE number 6554660 |
Statements
11 March 2016
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equation solved in closed form
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asymptotic behavior
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rational difference equation
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periodic solution
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On a fifth-order difference equation (English)
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The difference equation NEWLINE\[NEWLINEx_n=\frac{x_{n-3}x_{n-4}x_{n-5}}{x_{n-1}x_{n-2}(a_n+b_n x_{n-3}x_{n-4}x_{n-5})}NEWLINE\]NEWLINE with real coefficients and real initial conditions is considered. Explicit formulae for the well defined solutions are presented. A detailed analysis is made for the case when \(\{a_n\}_n\) and \(\{b_n\}_n\) are constant sequences; asymptotic behavior, constant and periodic solutions are discussed. Finally, the domain of undefinable solutions is analyzed.
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