# Asymptotic representations of solutions of the nonautonomous ordinary differential $n$-th order equations

## Mousa Jaber Abu Elshour and Vjacheslav Evtukhov

Address:

Mousa Jaber Abu Elshour, Department of Mathematics, Al al-bayt University, Mafraq, Jordan, Jordan-Irbid – 21110 P.O.Box 3867

Vjacheslav Evtukhov, Department of Differential Equations, Institute of Mathematics, Economics and Mechanics, Odessa I.I. Mechnikov National University, 65026, Odessa, Ukraine

E-mail:

drmousa67@yahoo.com

evmod@i.ua

Abstract: Asymptotic representations of some classes of solutions of nonautonomous ordinary differential $n$-th order equations which somewhat are close to linear equations are established.

AMSclassification: primary 34C11; secondary 26A12, 34E10, 34A34.

Keywords: nonlinear differential equations, P_\omega (\lambda _0)-solutions, asymptotic beaviour, regularly varying functions.

DOI: 10.5817/AM2017-1-1