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On the uniform asymptotic stability in functional-differential equations


Author: L. Z. Wen
Journal: Proc. Amer. Math. Soc. 85 (1982), 533-538
MSC: Primary 34K20
DOI: https://doi.org/10.1090/S0002-9939-1982-0660599-6
MathSciNet review: 660599
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Abstract: We consider a system of functional differential equations $ x'(t) = F(t,{x_t})$ and obtain conditions on a Liapunov functional to insure the uniform asymptotic stability of the zero solution.


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

  • [1] T. A. Burton, Uniform asymptotic stability in functional differential equations, Proc. Amer. Math. Soc. 68 (1978), 195-199. MR 0481371 (58:1489)
  • [2] T. Yoshizawa, Stability theory by Lyapunov's second method, Publ. Math. Soc. Japan, No. 9, Math. Soc. of Japan, Tokyo, 1966, pp. 183-192. MR 0208086 (34:7896)
  • [3] B. S. Razumikhin, Application of Liapunov's method to problems in the stability of systems with a delay, Avtomat. i Telemeh. 21 (1960), 740-749. (Russian)
  • [4] J. Kato, On Liapunov-Razumikhin type theorems for functional equations, Funkcial. Ekvac. 16 (1973), 225-239. MR 0355272 (50:7748)
  • [5] J. K. Hale, Theory of functional differential equations, Appl. Math. Sci., Vol. 3, Springer-Verlag, New York and Berlin, 1977, pp. 11-41. MR 0508721 (58:22904)
  • [6] N. N. Krasovskii, Stability of motion, Stanford Univ. Press, Stanford, Calif., 1963. MR 0147744 (26:5258)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1982-0660599-6
Keywords: Functional differential equations, Liapunov functionals, uniform asymptotic stability
Article copyright: © Copyright 1982 American Mathematical Society

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