INTEGRAL CONDITIONS ON THE ASYMPTOTIC STABILITY FOR THE DAMPED LINEAR-OSCILLATOR WITH SMALL DAMPING

Authors
HATVANI L
Citation
L. Hatvani, INTEGRAL CONDITIONS ON THE ASYMPTOTIC STABILITY FOR THE DAMPED LINEAR-OSCILLATOR WITH SMALL DAMPING, Proceedings of the American Mathematical Society, 124(2), 1996, pp. 415-422
Citations number
15
Categorie Soggetti
Mathematics, General",Mathematics,Mathematics
Journal title
Proceedings of the American Mathematical Society → ACNP
ISSN journal
00029939
Volume
124
Issue
2
Year of publication
1996
Pages
415 - 422
Database
ISI
SICI code
0002-9939(1996)124:2<415:ICOTAS>2.0.ZU;2-3
Abstract
The equation x '' + h(t)x' + k(2) x = 0 is considered under the assump tion 0 less than or equal to h(t) less than or equal to (h) over bar < infinity (t greater than or equal to 0). It is proved that lim sup(t- ->infinity) (t(-2/3) integral(0)(t) h) > 0 is sufficient for the asymp totic stability of x = x' = 0, and 2/3 is best possible here. This wil l be a consequence of a general result on the intermittent damping, wh ich means that h is controlled only on a sequence of non-overlapping i ntervals.