Oscillation of higher-order canonical delay differential equations: comparison theorems

In this work, we study the oscillatory properties of a higher-order neutral delay differential equation. By using the principle of comparison with equations of the first order we establish a set of new oscillation criteria for this equation under the canonical condition. Furthermore, the new criteria extend and complement some previous results in the literature. To that end, we compare these criteria by applying them to special cases of the equations under consideration in order to determine which one is the most efficient and least restrictive.