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Asymptotic integration of a certain second-order linear delay differential equation

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Abstract

We construct the asymptotic formulas for solutions of a certain linear second-order delay differential equation as independent variable tends to infinity. When the delay equals zero this equation turns into the so-called one-dimensional Schrödinger equation at energy zero with Wigner–von Neumann type potential. The question of interest is how the behaviour of solutions changes qualitatively and quantitatively when the delay is introduced in this dynamical model. We apply the method of asymptotic integration that is based on the ideas of the centre manifold theory in its presentation with respect to the systems of functional differential equations with oscillatory decreasing coefficients.

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Acknowledgments

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, 150003, 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 a certain second-order linear delay differential equation. Monatsh Math 182, 77–98 (2017). https://doi.org/10.1007/s00605-016-0980-3

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