Integral conditions on the asymptotic stability

for the damped linear oscillator

with small damping

Author:
L. Hatvani

Journal:
Proc. Amer. Math. Soc. **124** (1996), 415-422

MSC (1991):
Primary 34D20, 34A30

MathSciNet review:
1317039

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Abstract | References | Similar Articles | Additional Information

Abstract: The equation is considered under the assumption . It is proved that is sufficient for the asymptotic stability of , and is best possible here. This will be a consequence of a general result on the intermittent damping, which means that is controlled only on a sequence of non-overlapping intervals.

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Additional Information

**L. Hatvani**

Affiliation:
Bolyai Institute, Aradi vértanúk tere 1, Szeged, Hungary, H–6720

Email:
hatvani@math.u-szeged.hu

DOI:
https://doi.org/10.1090/S0002-9939-96-03266-2

Keywords:
Intermittent damping,
energy method

Received by editor(s):
January 7, 1994

Additional Notes:
The author was supported by the Hungarian National Foundation for Scientific Research with grant number 1157

Communicated by:
Hal L. Smith

Article copyright:
© Copyright 1996
American Mathematical Society