The recursive sequence \(x_{n+1} = g(x_{n},x_{n-1})/(A + x_{n})\) (Q1861776)
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scientific article; zbMATH DE number 1878863
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The recursive sequence \(x_{n+1} = g(x_{n},x_{n-1})/(A + x_{n})\) |
scientific article; zbMATH DE number 1878863 |
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The recursive sequence \(x_{n+1} = g(x_{n},x_{n-1})/(A + x_{n})\) (English)
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10 March 2003
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The author considers the second order nonlinear difference equation \[ x_{n+1}=\frac{g(x_n,x_{n-1})}{A+x_n},\qquad n=0,1,\dots, \] where \(A>0\) and \(g\: {\mathbb R}^2_+\to{\mathbb R}_+\) is a continuous function. The main result of the paper provides sufficient conditions on~\(g\) under which every positive solution tends to a period two solution.
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periodic solution
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positive solution
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second order nonlinear difference equation
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