Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Integral conditions on the asymptotic stability for the damped linear oscillator with small damping
HTML articles powered by AMS MathViewer

by L. Hatvani PDF
Proc. Amer. Math. Soc. 124 (1996), 415-422 Request permission

Abstract:

The equation $x''+h(t)x’+k^2x=0$ is considered under the assumption $0\le h(t)\le \overline {h}<\infty$ $(t\ge 0)$. It is proved that $\limsup _{t \to \infty }\left (t^{-2/3}\int _0 ^t h\right )>0$ is sufficient for the asymptotic stability of $x=x’=0$, and $2/3$ is best possible here. This will be a consequence of a general result on the intermittent damping, which means that $h$ is controlled only on a sequence of non-overlapping intervals.
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 34D20, 34A30
  • Retrieve articles in all journals with MSC (1991): 34D20, 34A30
Additional Information
  • L. Hatvani
  • Affiliation: Bolyai Institute, Aradi vértanúk tere 1, Szeged, Hungary, H–6720
  • MR Author ID: 82460
  • Email: hatvani@math.u-szeged.hu
  • 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
  • © Copyright 1996 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 124 (1996), 415-422
  • MSC (1991): Primary 34D20, 34A30
  • DOI: https://doi.org/10.1090/S0002-9939-96-03266-2
  • MathSciNet review: 1317039