Oscillation criteria for certain even order neutral delay differential equations with mixed nonlinearities (Q1724592)

Summary: We establish some oscillation criteria for the following certain even order neutral delay differential equations with mixed nonlinearities: \[ \left(r \left(t\right) \left|z^{\left(n - 1\right)} \left(t\right)\right|^{\alpha - 1} z^{\left(n - 1\right)} \left(t\right)\right)' + q_0(t) \left|(x \left(\tau_0 \left(t\right)\right)\right|^{\alpha - 1} x(\tau_0(t)) + q_1 \left(t\right) \left|(x(\tau_1(t))\right|^{\beta - 1} x(\tau_1(t)) + q_2 \left(t\right) \left|(x(\tau_2(t))\right|^{\gamma - 1} x(\tau_2(t)) = 0, \;t \geq t_0, \] where \(z(t) = x(t) + p(t) x(\sigma(t))\), \(n\) is even integer, and \(\gamma > \alpha > \beta > 0 \). Our results generalize and improve some known results for oscillation of certain even order neutral delay differential equations with mixed nonlinearities.