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Mosc. Math. J., 2018, Volume 18, Number 2, Pages 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

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.

DOI: https://doi.org/10.17323/1609-4514-2018-18-2-387-402

Full text: http://www.mathjournals.org/.../2018-018-002-008.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 34E05, 34E10
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Citation: V. S. Samovol, “Power geometry of a non-linear differential equation”, Mosc. Math. J., 18:2 (2018), 387–402

Citation in format AMSBIB
\Bibitem{Sam18}
\by V.~S.~Samovol
\paper Power geometry of a~non-linear differential equation
\jour Mosc. Math.~J.
\yr 2018
\vol 18
\issue 2
\pages 387--402
\mathnet{http://mi.mathnet.ru/mmj677}
\crossref{https://doi.org/10.17323/1609-4514-2018-18-2-387-402}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000439059900008}


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