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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
DOI: https://doi.org/10.1090/S0002-9939-1987-0877048-X
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?)

  • [1] E. A. Coddington and N. Levinson, Theory of ordinary differential equations, McGraw-Hill, New York, 1955. MR 0069338 (16:1022b)
  • [2] T. Yoshizawa, Stability theory by Lyapunov's second method, Math. Soc. Japan 9 (1966), 27-28. MR 0208086 (34:7896)
  • [3] H. Antosiewicz, A survey of Lyapunov's second method, Contributions to the Theory of Nonlinear Oscillations. IV, Ann. of Math. Studies, no. 41, Princeton Univ. Press, Princeton, N. J., 1958. MR 0102643 (21:1432)
  • [4] G. R. Sell, The structure of a flow in the vicinity of an almost periodic motion, J. Differential Equations 27 (1978), 359-393. MR 0492608 (58:11704)

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DOI: https://doi.org/10.1090/S0002-9939-1987-0877048-X
Article copyright: © Copyright 1987 American Mathematical Society

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