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In this paper we propose a method for stability studies of integro-differential systems. An application can be found in the regulation of testosterone level where distributed feedback control in the form of the integral term. The aim of the regulation is to hold testosterone concentration above the corresponding level. We have to choose the parameters of our distributed control in such proportion that the stability of the given system is preserved. [ABSTRACT FROM AUTHOR]

In this paper, new explicit tests for exponential stability of systems of second order equations are proposed. Our approach is based on nonoscillation of solutions of the corresponding diagonal scalar second order delay differential equations. [ABSTRACT FROM AUTHOR]

There are almost no results in mathematical literature on the exponential stability of third-order neutral delay differential equations. One of the main purposes of the paper is to fill this gap. We propose an approach to the study of stability for third-order delay differential equations based on AzbelevW-transform. On the basis of these results, new possibilities of stabilization by delay feedback input control are proposed. [ABSTRACT FROM AUTHOR]

The maximum principles present one of the classical parts in the qualitative theory of ordinary and partial differential equations. Although assertions about the maximum principles for functional differential equations can be interpreted in a corresponding sense as analogs of corresponding classical ones in the case of ordinary differential equations, they do not imply important corollaries, reached on the basis of finite dimensional fundamental systems. For example, results associated with the maximum principles in contrast with the cases of ordinary and even partial differential equations do not add so much in problems of existence and uniqueness. In this paper we obtain the maximum principles for functional differential equations and on this basis new results on existence and uniqueness of solutions for various boundary value problems are proposed. [ABSTRACT FROM AUTHOR]