International Journal of Stochastic Analysis

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International Journal of Stochastic Analysis / 1995 / Article

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Volume 8 |Article ID 416373 | 15 pages | https://doi.org/10.1155/S1048953395000219

Razumikhin's method in the qualitative theory of processes with delay

Anatoly D. Myshkis1

1Moscow State University of Communications, Department of Mathematics, Obraztsova St. 15, Moscow 101475, Russia

Received01 Jan 1995
Revised01 Mar 1995

Abstract

B.S. Razumikhin's concept in the qualitative theory of systems delay is clarified and discussed. Various ways of improvements of stability conditions are considered. The author shows that the guiding role of Lyapunov functions and demonstrates Razumikhin's method as a practical case of continuous version of the mathematical induction. Several examples demonstrate the obtained results.

Copyright © 1995 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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