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Journal of Applied Mathematics and Stochastic Analysis
Volume 8 (1995), Issue 3, Pages 233-247

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

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

Received 1 January 1995; Revised 1 March 1995

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.


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.