General permanence conditions for nonlinear difference equations of higher order (Q1378710)
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scientific article; zbMATH DE number 1115561
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | General permanence conditions for nonlinear difference equations of higher order |
scientific article; zbMATH DE number 1115561 |
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General permanence conditions for nonlinear difference equations of higher order (English)
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22 June 1998
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The paper deals with the equation \(x_n= f(x_{n-1}, x_{n-2},\dots, x_{n-m})\) for \(n\geq 1\), nonnegative \(f\) and nonnegative initial values. Under different conditions for \(f\) it is shown that the equation is permanent, i.e. that every solution is eventually confined in a fixed compact interval, which does not depend on the initial values. The results imply new oscillation theorems.
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permanence conditions
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nonlinear difference equations
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oscillation
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