Investigating Oscillatory Behavior in Third-Order Neutral Differential Equations with Canonical Operators

In this study, we aim to set new criteria regarding the asymptotic behavior of the neutral differential equation of the third order. These criteria are designed to ensure that this equation is oscillatory using comparisons with first-order differential equations and Riccati substitution. The results we obtained improve some of the results found in the literature. Some examples are provided to illustrate the applicability of our results and compare them with results found in some previous studies.