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.

**[1]**Earl A. Coddington and Norman Levinson,*Theory of ordinary differential equations*, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1955. MR**0069338****[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****[4]**George R. Sell,*The structure of a flow in the vicinity of an almost periodic motion*, J. Differential Equations**27**(1978), no. 3, 359–393. MR**0492608**

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1987-0877048-X

Article copyright:
© Copyright 1987
American Mathematical Society