New oscillation criteria for differential equations with sublinear and superlinear neutral terms

Authors

ALI MUHIB
ELMETWALLY M. ELABBASY
OSAMA MOAAZ

DOI

10.3906/mat-2012-11

Abstract

The aim of this article is to establish some new oscillation criteria for the differential equation of even-order of the form \begin{equation*} (r\left( l\right) (y^{\left( n-1\right) }\left( l\right) )^{\alpha })^{\prime }+f(l,x(\tau (l)))=0, \end{equation*} where $y\left( l\right) =x\left( l\right) +p\left( l\right) x^{\beta }\left( \sigma _{1}\left( l\right) \right) +h\left( l\right) x^{\delta }\left( \sigma _{2}\left( l\right) \right) $. By using Riccati transformations, we present new conditions for oscillation of the studied equation. Furthermore, two illustrative examples showing applicability of the new results are included.

Keywords

Sublinear and superlinear neutral terms, even-order differential equations, oscillation criteria

First Page

919

Last Page

928

Recommended Citation

MUHIB, ALI; ELABBASY, ELMETWALLY M.; and MOAAZ, OSAMA (2021) "New oscillation criteria for differential equations with sublinear and superlinear neutral terms," Turkish Journal of Mathematics: Vol. 45: No. 2, Article 20. https://doi.org/10.3906/mat-2012-11
Available at: https://journals.tubitak.gov.tr/math/vol45/iss2/20