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Turkish Journal of Mathematics

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.

First Page

919

Last Page

928

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