This article is cited in 1 scientific paper (total in 1 paper)
Center Manifold Method in the Asymptotic Integration Problem for Functional Differential Equations with Oscillatory Decreasing Coefficients. I
P. N. Nesterov
P. G. Demidov Yaroslavl State University,
Sovetskaya str., 14, Yaroslavl, 150000, Russia
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.
functional-differential equations, critical manifold, asymptotic integration.
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P. N. Nesterov, “Center Manifold Method in the Asymptotic Integration Problem for Functional Differential Equations with Oscillatory Decreasing Coefficients. I”, Model. Anal. Inform. Sist., 21:3 (2014), 5–34
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\paper Center Manifold Method in the Asymptotic Integration Problem for Functional Differential Equations with Oscillatory Decreasing Coefficients.~I
\jour Model. Anal. Inform. Sist.
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This publication is cited in the following articles:
P. N. Nesterov, “Metod tsentralnykh mnogoobrazii v zadache asimptoticheskogo integrirovaniya funktsionalno-differentsialnykh uravnenii s kolebatelno ubyvayuschimi koeffitsientami. II”, Model. i analiz inform. sistem, 21:5 (2014), 5–37
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