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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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.

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A comparision lemma for higher order trajectory derivatives
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by R. W. Gunderson PDF
Proc. Amer. Math. Soc. 27 (1971), 543-548 Request permission

Abstract:

A basic result from higher order differential inequalities is used to obtain a comparison lemma, useful when higher order trajectory derivatives of Liapunov functions are known.
References
    J. A. Yorke, Asymptotic properties of solutions using the second derivative of a Liapunov function, Ph.D. Dissertation, University of Maryland, College Park.
  • M. B. Kudaev, A study of the behaviour of the trajectories of systems of differential equations by means of Lyapunov functions, Dokl. Akad. Nauk SSSR 147 (1962), 1285–1287 (Russian). MR 0144038
  • Arthur R. Butz, Higher order derivatives of Liapunov functions, IEEE Trans. Automatic Control AC-14 (1969), 111–112. MR 0251315, DOI 10.1109/tac.1969.1099092
  • Jacek Szarski, Differential inequalities, Monografie Matematyczne, Tom 43, PaĹ„stwowe Wydawnictwo Naukowe, Warsaw, 1965. MR 0190409
  • Taro Yoshizawa, Stability theory by Liapunov’s second method, Publications of the Mathematical Society of Japan, vol. 9, Mathematical Society of Japan, Tokyo, 1966. MR 0208086
  • V. Lakshmikantham and S. Leela, Differential and integral inequalities. Vol. I. Academic Press, New York, 1969.
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Additional Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 27 (1971), 543-548
  • MSC: Primary 34.40
  • DOI: https://doi.org/10.1090/S0002-9939-1971-0273104-6
  • MathSciNet review: 0273104