On the difference equation \(x_{n+1} = x_nx_{n-k}/(x_{n-k+1}(a + bx_nx_{n-k}))\) (Q448573)
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scientific article; zbMATH DE number 6078659
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the difference equation \(x_{n+1} = x_nx_{n-k}/(x_{n-k+1}(a + bx_nx_{n-k}))\) |
scientific article; zbMATH DE number 6078659 |
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On the difference equation \(x_{n+1} = x_nx_{n-k}/(x_{n-k+1}(a + bx_nx_{n-k}))\) (English)
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7 September 2012
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Summary: We show that the difference equation \(x_{n+1} = x_nx_{n-k}/x_{n-k+1}(a + bx_nx_{n-k}), n \in \mathbb N_0\), where \(k \in \mathbb N\), the parameters \(a, b\) and initial values \(x_{-i}, i = \overline{0, k}\) are real numbers, can be solved in closed form considerably extending the results in the literature. By using obtained formulae, we investigate asymptotic behavior of well-defined solutions of the equation.
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