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
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