On the recursive sequence \(x_n=A+x_{n-k}^p/x_{n-1}^r\) (Q1040143)
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scientific article; zbMATH DE number 5637374
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the recursive sequence \(x_n=A+x_{n-k}^p/x_{n-1}^r\) |
scientific article; zbMATH DE number 5637374 |
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On the recursive sequence \(x_n=A+x_{n-k}^p/x_{n-1}^r\) (English)
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23 November 2009
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Summary: This paper studies the dynamic behavior of the positive solutions to the difference equation \(x_n=A+x_{n-k}^p/x_{n-1}^r\), \(n=1,2,\ldots,\) where \(A,p\) and \(r\) are positive real numbers, and the initial conditions are arbitrary positive numbers. We establish some results regarding the stability and oscillation character of this equation for \(p\in [0,1)\).
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