Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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



A comparision lemma for higher order trajectory derivatives

Author: R. W. Gunderson
Journal: Proc. Amer. Math. Soc. 27 (1971), 543-548
MSC: Primary 34.40
MathSciNet review: 0273104
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] J. A. Yorke, Asymptotic properties of solutions using the second derivative of a Liapunov function, Ph.D. Dissertation, University of Maryland, College Park.
  • [2] 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
  • [3] Arthur R. Butz, Higher order derivatives of Liapunov functions, IEEE Trans. Automatic Control AC-14 (1969), 111–112. MR 0251315
  • [4] Jacek Szarski, Differential inequalities, Monografie Matematyczne, Tom 43, Państwowe Wydawnictwo Naukowe, Warsaw, 1965. MR 0190409
  • [5] Taro Yoshizawa, Stability theory by Liapunov’s second method, Publications of the Mathematical Society of Japan, No. 9, The Mathematical Society of Japan, Tokyo, 1966. MR 0208086
  • [6] V. Lakshmikantham and S. Leela, Differential and integral inequalities. Vol. I. Academic Press, New York, 1969.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 34.40

Retrieve articles in all journals with MSC: 34.40

Additional Information

Keywords: High order trajectory derivatives, vector $ v$-functions, comparison lemma, stability properties
Article copyright: © Copyright 1971 American Mathematical Society

American Mathematical Society