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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 remark on a stability theorem of M. Marachkoff
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by John R. Haddock PDF
Proc. Amer. Math. Soc. 31 (1972), 209-212 Request permission

Abstract:

By placing certain conditions on $f(t,x)$ for the system of ordinary differential equations (1) \[ x’ = f(t,x),\;f(t,0) \equiv 0,\] Marachkoff weakened the conditions on the Liapunov function of the classical asymptotic stability theorem of Liapunov theory and obtained asymptotic stability of the zero solution of (1). Later, Massera gave a shorter proof of Marachkoff’s result. In this note we show that Marachkoff’s theorem can be proven without the use of one of the conditions.
References
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 31 (1972), 209-212
  • DOI: https://doi.org/10.1090/S0002-9939-1972-0288370-1
  • MathSciNet review: 0288370