Center Manifold Method in the Asymptotic Integration Problem for Functional Differential Equations with Oscillatory Decreasing Coefficients. II
https://doi.org/10.18255/1818-1015-2014-5-5-37
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 the solutions of the considered systems in a critical case. In the second part of the work we establish the existence of a critical manifold for the considered class of systems and study its main properties. We also investigate the asymptotic integration problem for a reduced system. We illustrate the proposed method with an example of constructing the asymptotics for the solutions of a certain scalar delay differential equation.
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. II. Modeling and Analysis of Information Systems. 2014;21(5):5-37. (In Russ.) https://doi.org/10.18255/1818-1015-2014-5-5-37
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