On the positive solutions of the difference equation \(x_{n+1}=\frac {ax_{n-1}} {1+bx_{n}x_{n-1}}\) (Q1888576)
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scientific article; zbMATH DE number 2118043
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the positive solutions of the difference equation \(x_{n+1}=\frac {ax_{n-1}} {1+bx_{n}x_{n-1}}\) |
scientific article; zbMATH DE number 2118043 |
Statements
On the positive solutions of the difference equation \(x_{n+1}=\frac {ax_{n-1}} {1+bx_{n}x_{n-1}}\) (English)
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23 November 2004
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The author presents a positive solution of the difference equation \(x_{n+1}=ax_{n-1}/(1+bx_{n}x_{n-1})\) where \(n\in\{0,1,2,\dots\}\) and \(a,b,x_{-1},x_0\) are nonnegative real numbers. He also proves that this equation has three equilibrium points: \(0\) and \(\pm\sqrt{(a-1)/b}\).
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positive solution
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difference equation
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equilibrium point
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recursive sequence
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