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Asymptotic Representations of Regularly Varying Pω(Y0, Y1, λ0)-Solutions of a Differential Equation of the Second Order Containing the Product of Different Types of Nonlinearities of the Unknown Function and its Derivative

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We establish necessary and sufficient conditions for the existence of regularly varying solutions of the second-order differential equations whose right-hand sides contain the product of a regularly varying nonlinearity of the unknown function and a rapidly varying nonlinearity of the derivative of the unknown function as the arguments tend either to zero or to infinity. Asymptotic representations of these solutions and their first-order derivatives are also found.

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Authors and Affiliations

  1. K. Ushyns’kyi South Ukrainian National Pedagogic University, Staroportofrankivs’ka Str., 26, Odessa, 65026, Ukraine

    O. O. Chepok

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  1. O. O. Chepok
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Correspondence to O. O. Chepok.

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Translated from Neliniini Kolyvannya, Vol. 25, No. 1, pp. 133–144, January–March, 2022.

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Chepok, O.O. Asymptotic Representations of Regularly Varying Pω(Y0, Y1, λ0)-Solutions of a Differential Equation of the Second Order Containing the Product of Different Types of Nonlinearities of the Unknown Function and its Derivative. J Math Sci 274, 142–155 (2023). https://doi.org/10.1007/s10958-023-06576-x

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  • DOI: https://doi.org/10.1007/s10958-023-06576-x

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