Stability results for difference equations of Volterra type (Q923277)
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scientific article; zbMATH DE number 4169328
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Stability results for difference equations of Volterra type |
scientific article; zbMATH DE number 4169328 |
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Stability results for difference equations of Volterra type (English)
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1990
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This paper is concerned with the stability of nonlinear Volterra difference equations of type \(x(n+1)-x(n)=f(n,x(n))+\sum^{n- 1}_{s=n_ 0}g(n,s,x(s)),\) \(x(n_ 0)=x_ 0\), with suitable maps f and g. By comparing the mentioned equation with certain linear Volterra difference equation, the authors are able to impose propriate conditions on f and g to ensure the asymptotic stability of the trivial solution of the above nonlinear difference equations.
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Lyapunov function
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nonlinear Volterra difference equations
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asymptotic stability
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