Power geometry of a non-linear differential equation. (English) Zbl 1418.34026

Samovol, V. S.

Mosc. Math. J. 18, No. 2, 387-402 (2018).

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.

MSC:

34A25	Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
34A34	Nonlinear ordinary differential equations and systems
34D05	Asymptotic properties of solutions to ordinary differential equations

Keywords:

power geometry; Emden-Fowler-type equation; continuable solution; non-oscillating solution; asymptotics; truncated equation