Denysenko N. Study of the solution properties for the systems of differential-functional equations with a linearly transformed argument

Existence of continuously differentiable solutions of the systems of differential-functional equations with linearly transformed argument is investigated and their properties are studied in the thesis. Conditions under which the study of the systems of linear nonhomogeneous differential-functional equations is reduced to the study of the systems of ordinary linear differential equations have been established. Conditions of the existence of a family of continuously differentiable solutions of the systems of linear and nonlinear differential-functional equations have been obtained and the method of their construction has been developed. The sufficient conditions of existence of bounded solutions of the systems of differential-functional equations with linear deviations of argument have been established. Furthermore, the method of construction has been suggested for such solutions of system and its asymptotic properties have been studied. The sufficient conditions of existence and uniqueness of continuous periodic solutions of the systems of linear and nonlinear differential-functional equations with linear deviations of argument have been obtained. The structure of asymptotic periodic solutions set of such systems equations has been researched.