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

• Main Author: Aydin Tiryaki
• Format: Article
• Language: English
• Published: University of Szeged 2009-11-01
• Series: Electronic Journal of Qualitative Theory of Differential Equations
• Online Access: http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=448

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.