Center Manifold Method in the Asymptotic Integration Problem for Functional Differential Equations with Oscillatory Decreasing Coefficients. I
https://doi.org/10.18255/1818-1015-2014-3-5-34
Abstract
In this paper, we study the asymptotic integration problem in the neighborhood of infinity for a certain class of linear functional differential systems. We construct the asymptotics for solutions of the considered systems in the critical case. Using the ideas of the center manifold method, we show the existence of the so-called critical manifold that is positively invariant for trajectories of the initial system. We establish that the asymptotics for solutions of the system on this manifold defines the asymptotics for all solutions of the initial system. In the first part of this work, we propose an algorithm for an approximate construction of the critical manifold. Moreover, we establish the unique solvability for auxiliary algebraic problems that occur within the algorithm implementation.
About the Author
P. N. Nesterov
P.G. Demidov Yaroslavl State University
Russian Federation
канд. физ.-мат. наук, доцент, Sovetskaya str., 14, Yaroslavl, 150000, Russia
Russian Federation
канд. физ.-мат. наук, доцент, Sovetskaya str., 14, Yaroslavl, 150000, Russia
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Review
For citations:
Nesterov P.N. Center Manifold Method in the Asymptotic Integration Problem for Functional Differential Equations with Oscillatory Decreasing Coefficients. I. Modeling and Analysis of Information Systems. 2014;21(3):5-34. (In Russ.) https://doi.org/10.18255/1818-1015-2014-3-5-34
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