Advanced Differential Equations with Canonical Operators: New Criteria for the Oscillation

Abstract

In this study, we use the integral averaging methodology, comparison with second-order differential equations, and the Riccati technique to determine the Philos-type and Hille–Nehari-type oscillation conditions of fourth-order advanced differential equations with canonical operators. In essence, these techniques supplement and generalize a wide range of established oscillation conditions. Two instance cases demonstrate the importance of our outcomes and their significant improvement.