We obtain asymptotic representations for one class of solutions of the systems of ordinary differential equations more general than systems of the Emden–Fowler type.
Similar content being viewed by others
References
D. D. Mirzov, “On the asymptotic properties of solutions of an Emden–Fowler-type system,” Differents. Uravn., 21, No. 9, 1498–1504 (1985).
D. D. Mirzov, “Some asymptotic properties of solutions of an Emden–Fowler-type system,” Differents. Uravn., 23, No. 9, 1519–1532 (1987).
D. D. Mirzov, Asymptotic Properties of the Solutions of Systems of Nonlinear Nonautonomous Ordinary Differential Equations [in Russian], Adygeiskoe Knizhn. Izd., Maikop (1993).
V. M. Evtukhov, “Asymptotic representations of regular solutions of a two-dimensional system of differential equations,” Dopov. Nats. Akad. Nauk Ukr., No. 4, 11–17 (2002).
V. M. Evtukhov, “Asymptotic representations of regular solutions of a semilinear two-dimensional system of differential equations,” Dopov. Nats. Akad. Nauk Ukr., No. 5, 11–17 (2002).
E. Seneta, Regularly Varying Functions, Springer, Berlin (1976).
V. Maric, Regular Variation and Differential Equations, Springer, Berlin (2000).
V. M. Evtukhov and V. M. Khar’kov, “Asymptotic representations of the solutions of essentially nonlinear second-order differential equations,” Differents. Uravn., 43, No. 9, 1311–1323 (2007).
V. N. Shinkarenko, “Asymptotic representations of solutions of an ordinary differential equation of the nth order with exponential nonlinearity,” Nelin. Kolyvannya, 7, No. 4, 562–573 (2004); English translation: Nonlin. Oscillations, 7, No. 4, 545–557 (2004).
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).
M. A. Belozerova, “Asymptotic properties of a class of solutions of essentially nonlinear second-order differential equations,” Mat. Stud., 29, No. 1, 52–62 (2008).
M. O. Bilozerova, “Asymptotic representations of the solutions of second-order differential equations with nonlinearities close (in a certain sense) to power nonlinearities,” Nauk. Visn. Cherniv. Univ., Issue 374, 34–43 (2008).
M. A. Belozerova, “Asymptotic representations of solutions of nonautonomous second-order differential equations with nonlinearities close to power-type nonlinearities,” Nelin. Kolyvannya, 12, No. 1, 3–15 (2009); English translation: Nonlin. Oscillations, 12, No. 1, 1–14 (2009).
V. M. Evtukhov and M. A. Belozerova, “Asymptotic representations of the solutions of essentially nonlinear nonautonomous second-order differential equations,” Ukr. Mat. Zh., 60, No. 3, 310–331 (2008); English translation: Ukr. Math. J., 60, No. 3, 357–383 (2008).
V. M. Evtukhov and A. M. Samoilenko, “Asymptotic representations of the solutions of nonautonomous ordinary differential equations with regularly varying nonlinearities,” Differents. Uravn., 47, No. 5, 628–650 (2011).
V. M. Evtukhov, Asymptotic Representations of the Solutions of Nonautonomous Ordinary Differential Equations [in Russian], Doctoral-Degree Thesis (Physics and Mathematics), Kiev (1998).
Author information
Authors and Affiliations
Additional information
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, No. 9, pp. 1165–1185, September, 2012.
Rights and permissions
About this article
Cite this article
Evtukhov, V.M., Shlepakov, O.R. Asymptotic representations of solutions of essentially nonlinear systems of ordinary differential equations with regularly and rapidly varying nonlinearities. Ukr Math J 64, 1326–1349 (2013). https://doi.org/10.1007/s11253-013-0720-y
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11253-013-0720-y