Matrix Linearization of Functional-Differential Equations of Point Type and Existence and Uniqueness of Periodic Solutions

Abstract

We study ω-periodic solutions of a functional-differential equation of point type that is ω-periodic in the independent variable. In terms of the right-hand side of the equation, we state easy-to-verify sufficient conditions for the existence and uniqueness of an ω-periodic solution and describe an iteration process for constructing the solution. In contrast to the previously considered scalar linearization, we use a more complicated matrix linearization, which permits extending the class of equations for which one can establish the existence and uniqueness of an ω-periodic solution.