Abstract
We establish asymptotic representations for the solutions of a class of nonlinear nonautonomous second-order differential equations.
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I. T. Kiguradze and T. A. Chanturiya, Asymptotic Properties of the Solutions of Nonautonomous Ordinary Differential Equations [in Russian], Nauka, Moscow (1990).
A. V. Kostin, “On the asymptotics of extendable solutions of the Emden-Fowler-type equations,” Dokl. Akad. Nauk SSSR, 200, No. 1, 28–31 (1971).
A. V. Kostin and V. M. Evtukhov, “Asymptotics of the solutions of one nonlinear differential equation,” Dokl. Akad. Nauk SSSR, 231, No. 5, 1059–1062 (1976).
V. M. Evtukhov, “On one nonlinear differential equation of the second order,” Dokl. Akad. Nauk SSSR, 233, No. 4, 531–534 (1977).
V. M. Evtukhov, “Asymptotic representations of the solutions of one class of second-order differential equations,” Soobshch. Akad. Nauk Gruz. SSR, 106, No. 3, 473–476 (1982).
V. M. Evtukhov, “Asymptotic properties of the solutions of one class of second-order differential equations,” Math. Nachr., 115, 215–236 (1984).
A. V. Kostin, “Asymptotics of the proper solutions of nonlinear ordinary differential equations,” Differents. Uravn., 28, No. 3, 524–526 (1987).
V. M. Evtukhov, “Asymptotic properties of the monotone solutions of one class of nonlinear differential equations of the nth order,” in: Reports of the Joint Seminar of the Institute of Applied Mathematics of the Tbilisi University, 3, No. 3, 62–65 (1988).
V. M. Evtukhov, “Asymptotic representations of the monotone solutions of a nonlinear nth-order differential equation of the Emden-Fowler type,” Dokl. Ros. Akad. Nauk, 234, No. 2, 258–260 (1992).
V. M. Evtukhov, “On one class of monotone solutions of a nonlinear nth-order differential equation of the Emden-Fowler type,” Soobshch. Akad. Nauk Gruz. SSR, 145, No. 2, 269–273 (1992).
V. M. Evtukhov, “Asymptotics of the solutions of one semilinear differential equation of the second order,” Differents. Uravn., 26, No. 5, 776–787 (1990).
P. K. Wong, “Existence and asymptotic behavior of proper solutions of a class of second-order nonlinear differential equations,” Pacif. J. Math., 13, 737–760 (1963).
V. Marić and M. Tomić, “Asymptotic properties of solutions of the equation y″ = f(x) Φ(y),” Math. Z., 146, 261–266 (1976).
S. D. Talliaferro, “Asymptotic behavior of the solutions of the equation y″ = Φ(t) f(y),” SIAM J. Math. Anal., 12, No. 6, 1–24 (1981).
V. M. Evtukhov and L. A. Kirillova, “Asymptotic representations of solutions of nonlinear second-order differential equations,” Mem. Different. Equat. Math. Phys., 30, 153–158 (2003).
L. O. Kirillova, “Asymptotic properties of the solutions of nonlinear second-order differential equations close to the Emden-Fowler equations,” Nauk. Visn. Cheniv. Univ., Ser. Mat., Issue 228, 30–35 (2004).
V. M. Evtukhov and L. A. Kirillova, “On the asymptotics of solutions of nonlinear second-order differential equations,” Differents. Uravn., 41, No. 8, 1053–1061 (2005).
L. A. Kirillova, “On the asymptotics of solutions of nonlinear second-order differential equations,” Nelin. Kolyv., 8, No. 1, 18–28 (2005).
V. M. Evtukhov, “On the solutions of real nonautonomous systems of quasilinear differential equations vanishing at infinity,” Differents. Uravn., 39, No. 4, 433–444 (2003).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 3, pp. 310–331, March, 2008.
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Evtukhov, V.M., Belozerova, M.A. Asymptotic representations of the solutions of essentially nonlinear nonautonomous second-order differential equations. Ukr Math J 60, 357–383 (2008). https://doi.org/10.1007/s11253-008-0063-2
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DOI: https://doi.org/10.1007/s11253-008-0063-2