Razumikhin's method in the qualitative theory of processes with delay
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.
functional differential equations of retarded type
scientific article; zbMATH DE number 794427