Oscillation of second order differential equations with mixed nonlinearities

By refining the standard integral averaging technique, in this paper, new oscillation criteria as well as interval oscillation criteria are established for the second order delay differential equation with mixed nonlinearities \begin{equation*} (r(t)|x\prime(t)|a-1x\prime(t))\prime+q0(t)|x(t0(t))|a-1x(t0(t)) +\sum\limitsi = 1nqi(t)|x(ti(t))|ai-1x(ti(t)) = 0, \end{equation*} where a>0, ai>0, i = 1,2,\cdots,n. Our results generalize and improve the known results in the literature. Examples are also given to illustrate the importance of our results.