Oscillation criteria for even order delay differential equations with damping (Q879451)

The author establishes oscillation criteria for the delay differential equation \[ \begin{multlined} (r(t)|x^{(n-1)}(t)|^{\alpha- 1} x^{(n- 1)}(t))'+ p(t)|x^{(n-1)}(t)|^{\alpha- 1} x^{(n- 1)}(t)+\\ f(t, x(\tau_{01}(t)),\dots, x(\tau_{0m}(t)),\dots, x^{(n- 1)}(\tau_{n- 11}(t)),\dots, x^{(n- 1)}(\tau_{n-1m}(t))= 0,\end{multlined} \] where \(\alpha> 0\) is a fixed constant, \(n\) is an even number. The results are based on extensions of the integral averaging technique.