We establish necessary and sufficient conditions for the existence of Pω (Y0 ,Y1, λ0)-solutions of one class of second-order differential equations with rapidly and regularly varying nonlinearities. This result is a natural generalization of the results of previous investigations carried out by V. М. Evtukhov and his school. We also established the asymptotic representations of these solutions and their first-order derivatives.
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 61, No. 2, pp. 26–37, April–June, 2018.
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Chepok, О.О. Asymptotic Representations of Rapidly Varying Solutions of Second-Order Differential Equations with Rapidly and Regularly Varying Nonlinearities. J Math Sci 253, 24–39 (2021). https://doi.org/10.1007/s10958-021-05210-y
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DOI: https://doi.org/10.1007/s10958-021-05210-y