A note on topological dynamics and limiting equations
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- by S. M. Shamim Imdadi and M. Rama Mohana Rao PDF
- Proc. Amer. Math. Soc. 40 (1973), 154-158 Request permission
Abstract:
A theorem on uniform asymptotic stability of the null solution of a system of differential equations is proved while assuming that the null solution of a limiting equation is uniformly asymptotically stable. This generalizes some of the results of L. Markus.References
- John L. Kelley, General topology, D. Van Nostrand Co., Inc., Toronto-New York-London, 1955. MR 0070144
- L. Markus, Asymptotically autonomous differential systems, Contributions to the theory of nonlinear oscillations, vol. 3, Annals of Mathematics Studies, no. 36, Princeton University Press, Princeton, N.J., 1956, pp. 17–29. MR 0081388
- George R. Sell, Nonautonomous differential equations and topological dynamics. I. The basic theory, Trans. Amer. Math. Soc. 127 (1967), 241–262. MR 212313, DOI 10.1090/S0002-9947-1967-0212313-2
- George R. Sell, Nonautonomous differential equations and topological dynamics. I. The basic theory, Trans. Amer. Math. Soc. 127 (1967), 241–262. MR 212313, DOI 10.1090/S0002-9947-1967-0212313-2 —, Non-autonomous differential equations as dynamical systems, Proc. Internat. Sympos. Differential Equations and Dynamical Systems (Puerto Rico, 1965), Academic Press, New York, 1967, pp. 531-536.
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 40 (1973), 154-158
- MSC: Primary 34C35; Secondary 54H20
- DOI: https://doi.org/10.1090/S0002-9939-1973-0322274-1
- MathSciNet review: 0322274