Vjacheslav M. Evtukhov and Kateryna S. Korepanova

Asymptotic Behaviour of Solutions of One Class of n-th Order Differential Equations

abstract:
We obtain the existence conditions and asymptotic representations of a certain class of power-mode solutions of a binomial non-autonomous n-th order ordinary differential equation with regularly varying nonlinearities and their derivatives of order up to n-1.

Mathematics Subject Classification: 34D05, 34C11

Key words and phrases: Ordinary differential equations, higher order, asymptotics of solutions, regularly varying nonlinearities