An oscillation theorem for a class of second-order forced neutral delay differential equations with mixed nonlinearities

A class of second-order forced neutral delay differential equation with mixed nonlinearities (r(t)|x′(t)+px′(t−σ)|α−1(x′(t)+px′(t−σ)))′+q0(t)|x(τ0(t))|α−1x(τ0(t))+∑i=1nqi(t)|x(τi(t))|βi−1x(τi(t))=e(t)sgn(x(t)) is investigated in this paper. Using a new method, we obtain some new sufficient conditions for the oscillation of the above equation, and some known oscillation criteria have been extended.