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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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Asymptotic stability for some critical autonomous differential equations
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by Elliot Winston PDF
Proc. Amer. Math. Soc. 44 (1974), 385-388 Request permission

Abstract:

Liapunov functions are constructed and used to prove stability theorems for critical autonomous systems in which the linear part of the right-hand side has a zero eigenvalue.
References
  • Jack K. Hale, Ordinary differential equations, Pure and Applied Mathematics, Vol. XXI, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1969. MR 0419901
  • J. P. LaSalle and S. Lefschetz, Stability by Liapunov’s direct method, with applications, Math. in Science and Engineering, vol. 4, Academic Press, New York, 1961. MR 24 #A2712. A. M. Liapunov, Problème général de la stabilité du mouvement, Ann. of Math. Studies, no. 17, Princeton Univ. Press, Princeton, N.J.; Oxford Univ. Press, London, 1947. MR 9, 34.
  • Walter Leighton, On the construction of Liapunov functions for certain autonomous nonlinear differential equations, Contributions to Differential Equations 2 (1963), 367–383 (1963). MR 153927
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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 44 (1974), 385-388
  • MSC: Primary 34D05
  • DOI: https://doi.org/10.1090/S0002-9939-1974-0344614-0
  • MathSciNet review: 0344614