Oscillation criteria for a certain second-order nonlinear differential equations with deviating arguments

A. Tiryaki, Izmir University, Uckuyular, Izmir, Turkey

E. J. Qualitative Theory of Diff. Equ., No. 61. (2009), pp. 1-11.

Abstract: In this paper, by using the generalized Riccati technique and the integral averaging technique, some new oscillation criteria for certain second order retarded differential equation of the form
\begin{equation*}
\left( r\left( t\right) \left\vert u^{\prime }\left( t\right) \right\vert
^{\alpha -1}u^{\prime }\left( t\right) \right) ^{\prime }+p\left( t\right)
f\left( u\left( \tau \left( t\right) \right) \right) =0
\end{equation*}
are established. The results obtained essentially improve known results in the literature and can be applied to the well known half-linear and Emden-Fowler type equations.

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