Razumikhin's method in the qualitative theory of processes with delay
type: Item
instance of: scholarly article
title: Razumikhin's method in the qualitative theory of processes with delay
zbMATH Open document ID: 0829.34069
DOI: 10.1155/S1048953395000219
author: A. D. Myshkis
published in: Journal of Applied Mathematics and Stochastic Analysis
publication date: 1996-01-17T00:00:00Z
full work available at URL: https://eudml.org/doc/47327
review text: A survey on Razumikhin's method in the qualitative theory for systems of differential equations with delay is given. This concept is applied to functional differential equations of retarded type which is an extension of the Lyapunov functionals to such equations. Razumikhin's method improves the stability conditions in more general situations, as the ``impossibility of the first breakdown''. This approach is analogous to the mathematical induction method for continuous processes. Using this method many parameter estimates of retarded differential equations guaranteeing stability can be made more accurate. Some applications of Razumikhin's method and some examples are considered.
reviewed by: Angela Slavova
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34K99
Mathematics Subject Classification ID: 93D20
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 37C75
Mathematics Subject Classification ID: 93D05
zbMATH DE Number: 794427
zbMATH Keywords: Razumikhin's method
zbMATH Keywords: functional differential equations of retarded type
zbMATH Keywords: Lyapunov functionals
MaRDI profile type: Publication
OpenAlex ID: W1984558460
description: scientific article; zbMATH DE number 794427