Oscillation results for third order nonlinear neutral differential equations of mixed type

Ethiraju Thandapania,* and Renu Ramab

Oscillation results for third order nonlinear neutral differential equations of mixed type

Authors :

Ethiraju Thandapani^a,* and Renu Rama^b

Author Address :

^a,bRamanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai -600 005, India.

*Corresponding author.

Abstract :

Some oscillation results are obtained for the third order nonlinear mixed type neutral differential equations of the form
\begin{equation}
((x(t)+b(t)x(t-\tau_1)+c(t)x(t+\tau_2))^\alpha)’’’=q(t)x^\beta(t-\sigma_1)+p(t)x^\gamma(t+\sigma_2), \ t \geq t_0
\nonumber\end{equation}
where $\alpha, \ \beta$ and $\gamma$ are ratios of odd positive integers $\tau_1,\ \tau_2, \ \sigma_1$ and $\sigma_2$ are positive constants.

Keywords :

Oscillation, third order, neutral differential equations.

DOI :

Article Info :

Received : November 11, 2012; Accepted : January 07, 2013.