The conditions of existence and asymptotic representations as t ↑ 𝜔 (𝜔 ≤ + ∞) are obtained for one class of solutions of nonautonomous differential equations of the nth order asymptotically close, in a certain sense, to equations with regularly varying nonlinearities.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 71, No. 12, pp. 1626–1646, December, 2019.
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Evtukhov, V.M., Droggina, A. Asymptotic Representations for the Solutions of Nonautonomous Ordinary Differential Equations. Ukr Math J 71, 1865–1887 (2020). https://doi.org/10.1007/s11253-020-01753-6