The existence of oscillatory solutions to fourth-order differential equations with multiple delays is investigated in this paper. The comparison method and the Riccati method are used to create new oscillation conditions. The results we have got, when compared to some studies in the literature, not only enhance the conditions for the oscillation of the examined equations, but they also expand some of the results that have already been published. Some examples are provided to illustrate the results.

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.