We determine asymptotic representations for the solutions of one class of second-order differential equations with rapidly and regularly varying nonlinearities.
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V. M. Evtukhov and N. G. Drik, “ Asymptotic behavior of solutions of a second-order nonlinear differential equation,” Georg. Math. J., 3, No. 2, 123–151 (1996).
V. M. Evtukhov and V. M. Kharkov, “Asymptotic representation of solutions of essentially nonlinear differential equations of second order,” Differents. Uravn., 43, No. 10, 1311–1323 (2007).
E. Seneta, Regularly Varying Functions [Russian translation], Nauka, Moscow (1985).
V. Maric, Regular Variation and Differential Equations, Springer Science & Business Media, Berlin (2000).
N. H. Bingham, C. M. Goldie, and J. L. Teugels, Regular Variation, Cambridge Univ. Press, Cambridge (1987).
V. M. Evtukhov and A. M. Klopot, “Asymptotic behavior of solutions of ordinary differential equations of order n with regularly varying nonlinearities,” Differents. Uravn., 50, No. 5, 584–600 (2014).
V. M. Evtukhov and A. M. Samoilenko, “Conditions for the existence of solutions of real nonautonomous systems of quasilinear differential equations vanishing at a singular point,” Ukr. Mat. Zh., 62, No. 1, 52–80 (2010); English translation: Ukr. Math. J., 62, No. 1, 56–86 (2010).
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Translated from Neliniini Kolyvannya, Vol. 20, No. 4, pp. 549–563, October–December, 2017.
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Chepok, O.O. Asymptotic Representations for the Solutions of Second-Order Differential Equations with Rapidly and Regularly Varying Nonlinearities. J Math Sci 238, 316–332 (2019). https://doi.org/10.1007/s10958-019-04238-5
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DOI: https://doi.org/10.1007/s10958-019-04238-5