Some stability conditions for scalar Volterra difference equations (Q2809650)
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scientific article; zbMATH DE number 6587415
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some stability conditions for scalar Volterra difference equations |
scientific article; zbMATH DE number 6587415 |
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Some stability conditions for scalar Volterra difference equations (English)
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30 May 2016
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linear Volterra difference and differential equations
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boundedness of solutions
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stability
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exponential stability
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numerical example
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This article deals with the following scalar linear difference equation NEWLINE\[NEWLINEx(n + 1) = x(n) = -a(n) + \sum_{k=1}^nA(n,k)x(k) + f(n)NEWLINE\]NEWLINE and its continuous analogue NEWLINE\[NEWLINE\dot{x}(t) = -a(t)x(t) + \int_0^t A(t,s)x(s) \, ds + f(t).NEWLINE\]NEWLINE Some natural conditions for \(A(n,k)\) and \(A(t,s)\) are presented that guarantee the boundedness of all solutions and conditions that guarantee the exponential decrease of all solutions for these equations. Some numerical examples are presented.
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