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

Matrix Linearization of Functional-Differential Equations of Point Type and Existence and... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

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

Differential Equations , Volume 54 (10) – Nov 16, 2018

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References (10)

Publisher
Springer Journals
Copyright
Copyright © 2018 by Pleiades Publishing, Ltd.
Subject
Mathematics; Ordinary Differential Equations; Partial Differential Equations; Difference and Functional Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1134/S0012266118100014
Publisher site
See Article on Publisher Site

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.

Journal

Differential EquationsSpringer Journals

Published: Nov 16, 2018

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