Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A note on topological dynamics and limiting equations


Authors: S. M. Shamim Imdadi and M. Rama Mohana Rao
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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] J. L. Kelley, General topology, Van Nostrand, Princeton, N.J., 1955. MR 16, 1136. MR 0070144 (16:1136c)
  • [2] L. Markus, Asymptotically autonomous differential systems, Contributions to Nonlinear Oscillations, Vol. 3, Ann. of Math. Studies, no. 36, Princeton Univ. Press, Princeton, N.J., 1956, pp. 17-29. MR 18, 394. MR 0081388 (18:394a)
  • [3] G. R. Sell, Non-autonomous differential equations and topological dynamics. I. The basic theory, Trans. Amer. Math. Soc. 127 (1967), 241-262. MR 35 #3187a. MR 0212313 (35:3187a)
  • [4] -, Non-autonomous differential equations and topological dynamics. II. Limiting equations, Trans. Amer. Math. Soc. 127 (1967), 263-283. MR 35 #3187b. MR 0212314 (35:3187b)
  • [5] -, 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.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 34C35, 54H20

Retrieve articles in all journals with MSC: 34C35, 54H20


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0322274-1
Keywords: Limiting equation, admissible function, regular function
Article copyright: © Copyright 1973 American Mathematical Society

American Mathematical Society