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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Asymptotic stability in functional-differential equations by Liapunov functionals


Author: Bo Zhang
Journal: Trans. Amer. Math. Soc. 347 (1995), 1375-1382
MSC: Primary 34K20
MathSciNet review: 1264834
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider the asymptotic stability in a system of functional differential equations $ x'(t) = F(t,{x_t})$ by Liapunov functionals $ V$. The work generalizes some well-known results in the literature in that we only require the derivative of $ V$ to be negative definite on a sequence of intervals $ {I_n} = [{S_n},{t_n}]$. We also show that it is not necessary to require a uniform upper bound on $ V$ for nonuniform asymptotic stability.


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.
  • [2] -, Stability and periodic solutions of ordinary and functional differential equations, Academic Press, Orlando, 1985.
  • [3] T. A. Burton and L. Hatvani, Stability theorems for nonautonomous functional differential equations by Liapunov functionals, Tôhoku Math. J. 41 (1989), 65-104.
  • [4] -, On nonuniform asymptotic stability for nonautonomous functional differential equations, Differential and Integral Equations 2 (1990), 285-293.
  • [5] T. A. Burton and G. Makay, Asymptotic stability for functional differential equations, Acta Math. Hungar. 65 (1994), 243-251.
  • [6] J. Hale, Theory of functional differential equations, Springer-Verlag, New York, 1977.
  • [7] J. Kato, A conjecture in Liapunov method for functional differential equations, Preprint.
  • [8] T. Yoshizawa, Stability by Liapunov's second method, Math. Soc. Japan, Tokyo, 1966.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1995-1264834-9
PII: S 0002-9947(1995)1264834-9
Keywords: Functional differential equations, Liapunov functionals, asymptotic stability
Article copyright: © Copyright 1995 American Mathematical Society