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Moscow Mathematical Journal, 2018, Volume 18, Number 2, Pages 387–402
DOI: https://doi.org/10.17323/1609-4514-2018-18-2-387-402 (Mi mmj677) 		 
Power geometry of a non-linear differential equation

V. S. Samovol

National Research University Higher School of Economics, 20, Myasnitskaya ul., Moscow, Russia
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DOI: https://doi.org/10.17323/1609-4514-2018-18-2-387-402
Abstract: In this article the solutions of Emden–Fowler-type equations of any order are studied using methods of power geometry. It is shown that these methods can be successfully applied in the study of asymptotic behaviour of the solutions. Also, we find conditions for the existence (nonexistence) of solutions of new types having non-power (power-logarithmic) asymptotics. Some numerical characteristics of such solutions are given.
Key words and phrases: power geometry, Emden–Fowler-type equation, continuable solution, non-oscillating solution, asymptotics, truncated equation.
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Document Type: Article
MSC: 34E05, 34E10
Language: English
Citation: V. S. Samovol, “Power geometry of a non-linear differential equation”, Mosc. Math. J., 18:2 (2018), 387–402
Citation in format AMSBIB
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