On the positive solutions of the difference equation \(x_{n+1}=(x_{n-1})/(1+x_{n} x_{n-1})\). (Q1428174)
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scientific article; zbMATH DE number 2056325
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the positive solutions of the difference equation \(x_{n+1}=(x_{n-1})/(1+x_{n} x_{n-1})\). |
scientific article; zbMATH DE number 2056325 |
Statements
On the positive solutions of the difference equation \(x_{n+1}=(x_{n-1})/(1+x_{n} x_{n-1})\). (English)
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14 March 2004
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The author obtains the exact expression of the positive solutions of the difference equation \[ x_{n+1}=\frac{x_{n-1}}{1+x_nx_{n-1}}, \quad n=0,1,2,\dots, \] where \(x_{-1}\) and \(x_0\) are two positive real numbers. From this expression it is deduced that the constant solution 0 is the unique equilibrium point.
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difference equations
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recursive sequence
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positive solutions
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equilibrium point
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