On the asymptotic behavior of a difference equation with maximum (Q937027)
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scientific article; zbMATH DE number 5314268
| Language | Label | Description | Also known as |
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| English | On the asymptotic behavior of a difference equation with maximum |
scientific article; zbMATH DE number 5314268 |
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On the asymptotic behavior of a difference equation with maximum (English)
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20 August 2008
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The author proves that the positive solutions of the second-order difference equation \[ x_n = \max \left\{ \frac A{x_{n-1}^\alpha}, \frac B{x_{n-2}^\beta} \right\} \] converge to the equilibrium state \(\max \{ A^{\frac 1{\alpha+1}}, B^{\frac 1{\beta+1}}\}\). There is also a comment concerning the higher order case.
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rational difference equations
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asymptotic behavior
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positive solutions
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second-order difference equation
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