Razumikhin's method in the qualitative theory of processes with delay. (1995)

• Record Type: Journal Article
• Authors: Myshkis, Anatoly D.
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 8:Number 3(1995)
• Page Start: 233
• Page End: 247
• Publication Date: 1995
• Subjects: functional-differential equation of retarded type -- qualitative theory -- systems with delay -- Razumikhin's method -- stability solution -- Lyapunov function -- first breakdown -- guiding function; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953395000219
• Languages: English
• ISSNs: 1048-9533

Abstract

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.