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Asymptotic integration of functional differential systems with oscillatory decreasing coefficients

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Abstract

We use the method of averaging and the extension of the Levinson fundamental theorem to study the problem of asymptotic integration of a class of linear functional differential systems that contain oscillatory decreasing coefficients. Moreover, we construct the asymptotics for solutions of the second order delay differential equation that is close, in some sense, to harmonic oscillator.

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Acknowledgments

The author would like to thank the professor Vladimir Burd for his valuable suggestions during the preparation of the paper. This research was supported in part by Ministry of Education and Science of Russian Federation (Federal Target Program “Scientific and scientific-pedagogical personnel of innovative Russia” in 2009–2013, State Contract No. \(\Pi \) 1229) and by the Government of the Russian Federation (Decree No. 220, Contract No. 11.G34.31.0053).

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  1. Department of Mathematics, Yaroslavl State University, Sovetskaya str. 14, 150000 , Yaroslavl, Russia

    Pavel Nesterov

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  1. Pavel Nesterov
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Correspondence to Pavel Nesterov.

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Communicated by A. Constantin.

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Nesterov, P. Asymptotic integration of functional differential systems with oscillatory decreasing coefficients. Monatsh Math 171, 217–240 (2013). https://doi.org/10.1007/s00605-012-0437-2

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  • DOI: https://doi.org/10.1007/s00605-012-0437-2

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