Abstract
We establish asymptotic representations for unbounded solutions of nonlinear nonautonomous differential equations of the third order that are close, in a certain sense, to equations of the Emden-Fowler type.
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I. T. Kiguradze and T. A. Chanturiya, Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations [in Russian], Nauka, Moscow (1991).
G. B. Abdul, Asymptotic Representations of Solutions of One Class of Nonlinear Third-Order Differential Equations [in Russian], Author’s Abstract of the Candidate-Degree Thesis (Physics and Mathematics), Odessa (1988).
A. V. Kostin, “Asymptotics of regular solutions of nonlinear ordinary differential equations,” Differents. Uravn., 23, No. 3, 524–526 (1987).
V. M. Evtukhov, “Asymptotic properties of monotone solutions of one class of nonlinear nth-order differential equations,” Dokl. Rasshir. Zased. Inst. Prikl. Mat. Tbil. Univ., 3, No. 3, 62–65 (1988).
V. M. Evtukhov, “Asymptotic representations of monotone solutions of a nonlinear nth-order differential equation of the Emden-Fowler type,” Dokl. Ross. 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 Gruzii, 145, No. 2, 269–273 (1992).
V. M. Evtukhov and A. A. Stekhun, “Asymptotic representations of unbounded solutions of nonlinear third-order differential equations,” Mat. Met. Fiz.-Mekh. Polya, 47, No. 4, 82–87 (2004).
V. M. Evtukhov, “On solutions of real nonautonomous systems of quasilinear differential equations that vanish at infinity,” Differents. Uravn., 39, No. 4, 433–444 (2003).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 10, pp. 1363–1375, October, 2007.
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Evtukhov, V.M., Stekhun, A.A. Asymptotic representations of solutions of one class of nonlinear nonautonomous differential equations of the third order. Ukr Math J 59, 1528–1543 (2007). https://doi.org/10.1007/s11253-008-0013-z
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DOI: https://doi.org/10.1007/s11253-008-0013-z