Properties of slowly varying solutions of significantly nonlinear differential equations of the second order

Gerzhanovska Greta Anatolyivna

Gerzhanovska Greta Anatolyivna ¹

¹ Department of Differential Equations, Geometry and Topology, Odesa I.I. Mechnikov National University, Odesa, 65037, Ukraine

Keywords: nonlinear differential equations

Download

Abstract

The necessary and sufficient conditions of the existence of a class of non- oscillatory solutions

of second-order differential equations with nonlinearities, that are in some sense near to regularly

varying nonlinearities are obtained. The asymptotic representations of such solutions and their

first derivatives are found too.

References

Seneta Е.RegularlyVaryingFunctions.–Lecture notes in Mathematics 508. SpringerVerlag, Berlin Heidelberg New York. – 1976. – 113 p.

Евтухов В.М. Асимптотические представления решений неавтономных обыкновенных дифференциальных уравнений: дис. докт. физ.-мат. наук: 01.01.02, Киев, 1998. 295 с.

Maric V. Regular variation and diﬀerential equations. – Lecture notes in Mathematics 1726. SpringerVerlag, Berlin Heidelberg New York. – 2000. – 128 p.

Евтухов В.М., Самойленко А.М. Условия существования исчезающих в особой точке решений у вещественных неавтономных систем квазилинейных дифференциальных уравнений// Укр. мат. журн. - 2010. - Т.62, №1. - С. 52 - 80.

Белозерова М. А., Гержановская Г. А. Асимптотические представления решений дифференциальных уравнений второго порядка с нелинейностями, в некотором смысле близкими к правильно меняющимся // Мат. Студiї. – 2015. – Т.44, №2. – C. 204 – 214.

Download

Cite

ACS Style: Gerzhanovska, G.A. Properties of slowly varying solutions of significantly nonlinear differential equations of the second order. Bukovinian Mathematical Journal. 2018, 5
AMA Style: Gerzhanovska GA. Properties of slowly varying solutions of significantly nonlinear differential equations of the second order. Bukovinian Mathematical Journal. 2018; 5(3-4).
Chicago/Turabian Style: Greta Anatolyivna Gerzhanovska. 2018. "Properties of slowly varying solutions of significantly nonlinear differential equations of the second order". Bukovinian Mathematical Journal. 5 no. 3-4.

Export

BibTex EndNote RIS