A Simplified Approach to Investigating the Oscillatory Behavior of Nonlinear Even-Order Neutral Differential Equations

This article explores the oscillation properties of solutions for higher-order nonlinear neutral functional differential equations. This study sought to establish applicable oscillation conditions for nonlinear NDDEs when α≠β. Our analysis focused on identifying the key asymptotic characteristics of positive solutions in the noncanonical case. Based on these properties, we developed a multi-conditional criterion that guarantees oscillation, thereby extending previously established results for second-order equations. Unlike previous results, which involved arbitrary constants and were thus difficult to apply, the criteria derived in this work do not contain such constants, making them directly applicable. Moreover, to overcome the complexity introduced by the multiple constraints of this criterion, we propose a new and previously unreported simplified oscillation condition. The effectiveness of this simplified criterion is demonstrated through an illustrative example.