Second-order nonlinear neutral differential equations with delay term: Novel oscillation theorems

This work aims to propose novel criteria to guarantee the oscillation of solutions for second-order differential equations. To analyze the oscillatory characteristics of the studied equation, new necessary conditions are introduced. We used a variety of analysis techniques to support these findings, forming fresh connections to tackle some issues that have impeded earlier studies. As a result, by using the Riccati transformation and the principles of comparison, we were able to acquire results that both expand upon and enhance those found in previous research. Several examples are presented to illustrate the significance of our findings.