Investigation of Oscillation Properties in Fourth‐Order Emden–Fowler Type Advanced Differential Equations: A Study on Canonical and Noncanonical Forms

ABSTRACT This paper examines the oscillatory behavior of a fourth‐order nonlinear differential equation in both canonical and noncanonical forms. Using a combination of comparison methods and integral averaging techniques, we establish novel criteria for the oscillation of solutions specifically to the canonical form of the studied equation. Without assuming any extra conditions, we also transform the noncanonical equation into a canonical representation, enabling us to apply previously derived criteria to assess the oscillation for this case. Our findings present novel results applicable to both forms of the studied equation, thus enhancing the current understanding in this area. Additionally, we illustrate the significance of our results with various examples, highlighting their superiority over known criteria in the existing literature.