Moscow Mathematical Journal
Volume 18, Issue 2, April–June 2018 pp. 387–402.
Power Geometry of a Non-Linear Differential Equation
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.
Authors:
V. S. Samovol (1)
Author institution:(1) National Research University Higher School of Economics, 20, Myasnitskaya ul., Moscow, Russia
Summary:
Keywords: Power geometry, Emden–Fowler-type equation, continuable solution, non-oscillating solution, asymptotics, truncated equation.
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