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On the Asymptotic Behavior of Solutions of Odd-Order Differential Equations with Oscillating Coefficients

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Abstract

We study the asymptotic behavior of solutions of an ordinary singular differential equation of arbitrary odd order. The potential in the equation can be either a rapidly oscillating function or a distribution. With the help of special quasiderivatives, the equation is reduced to a system of first-order differential equations, which is then reduced to \(L \)-diagonal form by a successive application of Hausdorff transformations.

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Funding

Ya.T. Sultanaev’s research was supported by the Ministry of Education and Science of the Republic of Kazakhstan, project no. AR08856104, and financially supported by the Ministry of Education and Science of the Russian Federation as part of the program of the Moscow Center for Fundamental and Applied Mathematics, agreement no. 075-15-2019-1621.

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Correspondence to Ya. T. Sultanaev, A. R. Sagitova or B. I. Mardanov.

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Translated by V. Potapchouck

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Sultanaev, Y.T., Sagitova, A.R. & Mardanov, B.I. On the Asymptotic Behavior of Solutions of Odd-Order Differential Equations with Oscillating Coefficients. Diff Equat 58, 712–715 (2022). https://doi.org/10.1134/S001226612205010X

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  • DOI: https://doi.org/10.1134/S001226612205010X