Oscillatory behavior for higher-order nonlinear differential equations in the canonical case

Abstract In this paper, we study the oscillation of a class of higher-order neutral nonlinear differential equations. We begin by establishing the relationship between the solution and its corresponding function. Then, by applying Riccati substitution along with some inequalities, we derive a set of sufficient conditions under which positive solutions do not exist, thus providing an oscillation criterion that guarantees the oscillation of all solutions to the equation under study. These criteria also improve upon related results in the literature. Examples are given to illustrate the significance of the established results.