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On Some Extension of Center Manifold Method to Functional Differential Equations with Oscillatory Decreasing Coefficients and Variable Delays

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Abstract

We propose an asymptotic integration method for certain class of functional differential systems. This class includes the delay differential equations with oscillatory decreasing coefficients and variable delays that are close to constants at infinity. Both the ideas of the centre manifold theory and the averaging method together with some classical asymptotic theorems are used to construct the asymptotics for solutions. We illustrate the asymptotic integration method by constructing the asymptotics for solutions of scalar differential equation with variable delay.

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Acknowledgements

The author is indebted to the referee for several helpful suggestions and pointing out the references [1, 11, 12, 15]. This research was supported by the grant of the President of the Russian Federation No. MK-4625.2016.1.

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  1. Department of Mathematics, Yaroslavl State University, Sovetskaya Str. 14, Yaroslavl, Russia, 150003

    Pavel Nesterov

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  1. Pavel Nesterov
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Correspondence to Pavel Nesterov.

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Nesterov, P. On Some Extension of Center Manifold Method to Functional Differential Equations with Oscillatory Decreasing Coefficients and Variable Delays. J Dyn Diff Equat 30, 1797–1816 (2018). https://doi.org/10.1007/s10884-017-9628-9

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  • DOI: https://doi.org/10.1007/s10884-017-9628-9

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