We establish conditions for the existence of one class of solutions of two-term nonautonomous second-order differential equations with rapidly varying nonlinearities and obtain the asymptotic representations for these solutions and their first-order derivatives as t ↑ ω(ω ≤ + ∞).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 69, No. 10, pp. 1345–1363, October, 2017.
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Evtukhov, V.M., Chernikova, A.G. Asymptotic Behavior of the Solutions of Ordinary Second-Order Differential Equations with Rapidly Varying Nonlinearities. Ukr Math J 69, 1561–1582 (2018). https://doi.org/10.1007/s11253-018-1455-6
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DOI: https://doi.org/10.1007/s11253-018-1455-6