Nonlinear neutral differential equations of second-order: Oscillatory properties

This paper investigates the oscillatory behavior of second-order differential equations featuring a mixed neutral term along with a $p$-Laplace differential operator. The analysis employs Riccati transformations and includes a comparative study with first-order equations, which facilitates the development of oscillation criteria. The findings culminate in a significant theorem that addresses the oscillation properties of these equations. In addition, two illustrative examples are presented to demonstrate the practical application of the established criteria.