Electron. J. Diff. Eqns., Vol. 1997(1997), No. 17, pp 1-6.

Stability of a linear oscillator with variable parameters

Alexander O. Ignatyev

A criterion of asymptotic stability for a linear oscillator with variable parameters is obtained. It is shown that this criterion is close to a necessary and sufficient conditions of asymptotic stability. An instability theorem is proved, and a mechanical example is considered.

Submitted June 20, 1997. Published October 29, 1997.
Math Subject Classification: 34D20, 70J25.
Key Words: differential equation, stable solution, Lyapunov function.

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Alexander O. Ignatyev
Institute for Applied Mathematics and Mechanics
R.Luxemburg Street 74, Donetsk-340114, Ukraine
e-mail: ignat@iamm.ac.donetsk.ua
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