On asymptotic behaviour of the difference equation \(x_{n+1} = \alpha+\frac{x_{n-1}^p}{x_n^p}\). (Q1432797)
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scientific article; zbMATH DE number 2076571
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On asymptotic behaviour of the difference equation \(x_{n+1} = \alpha+\frac{x_{n-1}^p}{x_n^p}\). |
scientific article; zbMATH DE number 2076571 |
Statements
On asymptotic behaviour of the difference equation \(x_{n+1} = \alpha+\frac{x_{n-1}^p}{x_n^p}\). (English)
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22 June 2004
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The authors investigate the oscillation with respect to the equilibrium, and the asymptotic behaviour of the positive solutions to the difference equation \[ x_{n+1}=\alpha+(x_{n-1}/x_n)^p,\, n=0,1,\dots, \] where \(\alpha\geq 0\) and \(p\geq 1\).
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difference equations
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asymptotic behaviour
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oscillatory solutions
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positive solutions
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0.98228043
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0.9413888
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0.93919086
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0.93511164
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0.9350457
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0.9267212
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