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Asymptotic Behavior of the Solutions of Essentially Nonlinear Nonautonomous Second-Order Differential Equations Close to Linear Functions

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For essentially nonlinear nonautonomous differential equations of the second order with nonlinearities close to regularly varying functions, we establish the conditions of existence of a sufficiently broad class of solutions that are close to linear functions as the argument approaches the critical point. Moreover, the exact asymptotic formulas for these solutions and their first-order derivatives are obtained. The number of these solutions is also determined. The accumulated results are illustrated for a more specific class of differential equations.

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Correspondence to M. O. Bilozerova.

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Translated from Neliniini Kolyvannya, Vol. 25, No. 1, pp. 3–13, January–March, 2022.

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Bilozerova, M.O., Herzhanovs’ka, H.A. Asymptotic Behavior of the Solutions of Essentially Nonlinear Nonautonomous Second-Order Differential Equations Close to Linear Functions. J Math Sci 274, 1–12 (2023).

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