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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Asymptotic stability for some critical autonomous differential equations


Author: Elliot Winston
Journal: Proc. Amer. Math. Soc. 44 (1974), 385-388
MSC: Primary 34D05
MathSciNet review: 0344614
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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 [Enhancements On Off] (What's this?)

  • [1] Jack K. Hale, Ordinary differential equations, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1969. Pure and Applied Mathematics, Vol. XXI. MR 0419901 (54 #7918)
  • [2] 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.
  • [3] 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.
  • [4] Walter Leighton, On the construction of Liapunov functions for certain autonomous nonlinear differential equations, Contributions to Differential Equations 2 (1963), 367–383 (1963). MR 0153927 (27 #3888)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1974-0344614-0
PII: S 0002-9939(1974)0344614-0
Article copyright: © Copyright 1974 American Mathematical Society