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The goal of this paper was to study the oscillations of a class of fourth-order nonlinear delay differential equations with a middle term. Novel oscillation theorems built on a proper Riccati-type transformation, the comparison approach, and integral-averaging conditions were developed, and several symmetric properties of the solutions are presented. For the validation of these theorems, several examples are given to highlight the core results.

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The oscillation criteria are investigated for all solutions of evenorder neutral differential equations. The obtained results are based on the new comparison theorems, that enable us to reduce the problem of the oscillation of the higher order equation to the oscillation of the first order equation. The obtained comparison principles essentially simplify the examination of the studied equations.

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