Asymptotic stability for some critical autonomous differential equations
Author:
Elliot Winston
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
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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.
- [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
- [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 153927
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 34D05
Retrieve articles in all journals with MSC: 34D05
Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1974-0344614-0
Article copyright:
© Copyright 1974
American Mathematical Society
