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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Preservation of uniform asymptotic stability under perturbations


Author: R. K. Miller
Journal: Proc. Amer. Math. Soc. 51 (1975), 155-158
MSC: Primary 45M10
MathSciNet review: 0372563
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Abstract: Suppose the trivial solution of the interval initial value problem for a linear, convolution, Volterra integrodifferential equation is uniformly asymptotically stable. If the kernel in this equation is integrable, then it is shown that this stability is preserved under perturbations which are nonantisipative and of order two or more.


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  • [1] J. M. Bownds and J. M. Cushing, On preserving stability of Volterra integral equations under a general class of perturbations, Math. Systems Theory 9 (1975), no. 2, 117–131. MR 0383025 (52 #3907)
  • [2] S. I. Grossman and R. K. Miller, Nonlinear Volterra integrodifferential systems with 𝐿¹-kernels, J. Differential Equations 13 (1973), 551–566. MR 0348417 (50 #915)
  • [3] R. K. Miller, Asymptotic stability properties of linear Volterra integrodifferential equations, J. Differential Equations 10 (1971), 485–506. MR 0290058 (44 #7243)
  • [4] -, Asymptotic stability and perturbations for linear integrodifferential systems, Delay and Functional Differential Equations and Their Applications, Academic Press, New York, 1972, pp. 257-268.
  • [5] R. K. Miller, Linear Volterra integrodifferential equations as semigroups, Funckcial. Ekvac. 17 (1974), 39–55. MR 0350511 (50 #3003)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0372563-1
PII: S 0002-9939(1975)0372563-1
Article copyright: © Copyright 1975 American Mathematical Society