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Total stability for neutral functional differential equations

Authors: A. F. Izé and A. A. Freiria
Journal: Proc. Amer. Math. Soc. 81 (1981), 437-442
MSC: Primary 34K20
MathSciNet review: 597658
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Abstract: The basic idea of this work is to use Lyapunov functionals to show that for neutral functional differential equations, uniform asymptotic stability implies total stability.

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

  • [1] M. A. Cruz and J. K. Hale, Stability of functional differential equations of neutral type, J. Differential Equations 7 (1970), 334-355. MR 0257516 (41:2166)
  • [2] J. K. Hale, Functional differential equations, Springer-Verlag, New York, 1977. MR 0466837 (57:6711)
  • [3] A. F. Izé and J. G. dos Reis, Stability of perturbed neutral functional differential equations, J. Nonlinear Analysis: Theory, Methods and Applications 2 (1978), 563-571. MR 512152 (80c:34081)
  • [4] J. Kato and Y. Sibuya, Catastrophic deformation of a flow and nonexistence of almost periodic solution, J. Fac. Sci. Univ. Tokyo Sect. IA 24 (1977), 267-280. MR 0466760 (57:6636)
  • [5] O. F. Lopes, a) Stability and forced oscillations, J. Math. Anal. Appl. 55 (1976), 686-698. b) Periodic solutions of perturbed neutral differential equations, J. Differential Equations 15 (1974), 70-76. MR 0446657 (56:4982)
  • [6] T. Yoshizawa, Stability theory by Lyapunov's second method, Publ. Math. Soc. Japan, no. 9, Math. Soc. Japan, Tokyo, 1966. MR 0208086 (34:7896)

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Keywords: Lyapunov functional, neutral functional differential equation, uniform stability, uniformly stable $ D$ operator, uniform asymptotic stability, total stability
Article copyright: © Copyright 1981 American Mathematical Society

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