Moscow Mathematical Journal

Volume 18, Issue 2, April–June 2018 pp. 387–402.

Power Geometry of a Non-Linear Differential Equation

Authors: V. S. Samovol (1)
Author institution:(1) National Research University Higher School of Economics, 20, Myasnitskaya ul., Moscow, Russia

Summary:

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 nonpower (power-logarithmic) asymptotics. Some numerical characteristics of such solutions are given.

2010 Math. Subj. Class. 34E05, 34E10.

Keywords: Power geometry, Emden–Fowler-type equation, continuable solution, non-oscillating solution, asymptotics, truncated equation.

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