Oscillation Criteria for Certain Second-Order Nonlinear Neutral DifferentialEquations of Mixed Type

Abstract

Some oscillation criteria are established for the second-order nonlinear neutral differential equations of mixed type ${\left[{\left(x\right(t)+p_{1}x(t-{\tau }_1)+p_{2}x(t+{\tau }_2\left)\right)}^{\gamma }\right]}^{\prime \prime }=q_1\left(t\right)x^{\gamma }(t-{\sigma }_1)+q_2\left(t\right)x^{\gamma }(t+{\sigma }_2)$, $t\ge t_0$, where $\gamma \ge 1$ is a quotient of odd positive integers. Our results generalize the results given in the literature.