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)



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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

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

  • [1] J. M. Bownds and J. M. Cushing, On preserving stability of Volterra integral equations under a general class of perturbations, SIAM J. Math. Anal. (to appear). MR 0383025 (52:3907)
  • [2] S. I. Grossman and R. K. Miller, Nonlinear Volterra integrodifferential systems with $ {L^1}$-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 44 #7243. 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 semi-groups, Funkcial. Ekvac 17 (1974), 39-55. MR 0350511 (50:3003)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 45M10

Retrieve articles in all journals with MSC: 45M10

Additional Information

Article copyright: © Copyright 1975 American Mathematical Society

American Mathematical Society