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.
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Original Russian Text © L.A. Beklaryan, F.A. Belousov, 2018, published in Differentsial’nye Uravneniya, 2018, Vol. 54, No. 10, pp. 1299–1312.
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Beklaryan, L.A., Belousov, F.A. Matrix Linearization of Functional-Differential Equations of Point Type and Existence and Uniqueness of Periodic Solutions. Diff Equat 54, 1271–1284 (2018). https://doi.org/10.1134/S0012266118100014
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DOI: https://doi.org/10.1134/S0012266118100014