Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
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
Full-text PDF Free Access

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, 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)

Similar Articles

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

Retrieve articles in all journals with MSC: 45M10

Additional Information

PII: S 0002-9939(1975)0372563-1
Article copyright: © Copyright 1975 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia