Stability of equations with delay
The paper is a survey of some works on the stability of linear functional-differential equations with delay by the participants in the Perm Seminar (Russia). It consists of an introduction and three sections. The first section is devoted to the variation of constants (the Cauchy) formula. By this formula the Cauchy problem for a functional-differential equation is reduced to a Volterra equation. The second section deals with the so-called \(D\)-property of functional equations with delay. To this property the reader is referred to the book [\textit{N. Azbelev, V. Maksimov} and \textit{L. Rakhmathullina}, Introduction to the theory of linear functional differential equations. Transl. from the Russian. Advanced Series in Mathematical Science and Engineering, 3, Atlanta, GA (1995; Zbl 0867.34051)]. Using the \(D\)-property, the authors state some theorems on stability. In the third section, applications of previous results to stability of ordinary (not functional) differential equations are given. The authors do not compare their method with the well-known results by A. Myshkis, J. Hale, V. Kolmanovskii, T. Yoneyama, etc.
linear functional-differential equations with delay
scientific article; zbMATH DE number 1175189