Asymptotic Behavior of Solutions of Ordinary Differential Equations of the  n th Order with Regularly Varying Nonlinearities

V. M. Evtukhov; A. G. Doroshenko

doi:10.1007/s10958-019-04536-y

Asymptotic Behavior of Solutions of Ordinary Differential Equations of the nth Order with Regularly Varying Nonlinearities

Authors: Evtukhov V.M.¹, Doroshenko A.G.¹
Affiliations:
1. Mechnikov Odessa National University
Issue: Vol 243, No 2 (2019)
Pages: 204-229
Section: Article
URL: https://journals.rcsi.science/1072-3374/article/view/243082
DOI: https://doi.org/10.1007/s10958-019-04536-y
ID: 243082

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Abstract
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Abstract

We establish conditions for the existence of some classes of solutions of nonautonomous differential equations of the nth order with regularly varying nonlinearities and asymptotic representations of these solutions and their derivatives up to order n – 1; inclusively, as t ↑ ω ( ω ≤ + ∞ ).

About the authors

V. M. Evtukhov

Mechnikov Odessa National University

Author for correspondence.
Email: melissa.delgado@springer.com
Ukraine, Dvoryanskaya Str. 2, Odessa, 65026

A. G. Doroshenko