Proceedings of the American Mathematical Society

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

 

 

On a converse result for Perron's theorem for asymptotic stability for nonlinear differential equations


Author: George Seifert
Journal: Proc. Amer. Math. Soc. 99 (1987), 733-736
MSC: Primary 34D20; Secondary 34D05
MathSciNet review: 877048
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Abstract: Two fairly simple proofs of a converse of Perron's classical theorem for the exponential asymptotic stability of the trivial solution of a nonlinear system of ordinary differential equations are given.


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

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  • [2] 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
  • [3] H. A. Antosiewicz, A survey of Lyapunov’s second method, Contributions to the theory of nonlinear oscillations, Vol. IV, Annals of Mathematics Studies, no. 41, Princeton University Press, Princeton, N.J., 1958, pp. 141–166. MR 0102643
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DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0877048-X
Article copyright: © Copyright 1987 American Mathematical Society