Analysis of Oscillation in Neutral Differential Equations of Even Order with Specific Delay Properties

Abstract

This research addresses a limitation in the current "Kamenev-Type" criteria used by mathematicians to study the behavior (oscillation) of solutions to a specific kind of equation (even order neutral differential equations). These equations describe scenarios where the rate of change depends on both the current state and a delayed version of it. By tackling this shortcoming, the paper introduces new and enhanced results for understanding oscillation in these equations. This advancement not only refines the "Kamenev-Type" criteria but also surpasses many other established methods for analyzing oscillation in this area of mathematics.