A damped oscillator with piecewise constant time delay (Q2763911)
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scientific article; zbMATH DE number 1693383
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A damped oscillator with piecewise constant time delay |
scientific article; zbMATH DE number 1693383 |
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22 January 2002
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piecewise constant delay
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oscillation
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periodic solution
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A damped oscillator with piecewise constant time delay (English)
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The authors study the asymptotic behavior of the solutions to the second-order differential equation with piecewise constant argument NEWLINE\[NEWLINEx''(t)+ \omega^2 x(t)= -bx'([t- 1]),NEWLINE\]NEWLINE where \(b\), \(\omega> 0\) are constants and \([\cdot]\) denotes the greatest-integer function. Among others, they show that the given delay equation may generate periodic or unbounded solutions whereas all solutions to the corresponding equation without delay tend to zero as \(t\to\infty\).
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