Abstract:

In this work, we study the oscillation of the second order Nonlinear Neutral Differential Equations with Distributed Delay

$(r(t)|z'(t)|^{\alpha-1}z'(t))'+\int^{d}_{c}f(t, x(\sigma(t, \xi))){\rm d}\xi=0, $

where $t\geq t_{0}, ~z(t)=x(t)+\int^{b}_{a}p(t, \xi)x(\tau(t, \xi)){\rm d}\xi $. we establish some new oscillation criteria for the above equation. These results extend and improve some known results in the cited literature. Also, our results are illustrated with some examples. It is shown that the theorem has some advantages over the existing literature.

Key words: Distributed delay, Half-linear, Oscillation criterion, Generalized Riccati inequality