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In this paper, we present some oscillation criteria for the second order half-linear neutral delay differential equation with ``maxima" of the from \begin{equation*} \left(r(t)((x(t)+p(t)x(\tau(t)))')^{\alpha}\right)'+q(t) \max_{[\sigma(t),\;t]}x^{\alpha}(s)=0 \end{equation*} under the condition $\int_{t_0}^{\infty}\frac{1}{r^{1/ \alpha}(t)}dt<\infty.$ The results obtained here extend and complement to some known results in the literature. Examples are provided in support of our results.

Oscillation results for second order half-linear neutral delay differential equations with "maxima"