Monotonic and oscillatory features of solutions to general functional differential equations with a neutral-delay argument

Abstract

This work is concerned with establishing several criteria for investigating the oscillatory features of solutions to a class of second-order neutral differential equations. This type of equation is rich in interesting analytical points as well as its applications in physical and engineering fields. Based on some new monotonic properties, we derive sufficient conditions for oscillation using the comparison principle and Riccati substitutions. The approach used allows us to remove some restrictions that are usually imposed on the coefficients of neutral differential equations in previous works. Moreover, some of the new criteria provide a sharp result when applied to the Euler differential equation. We support the theoretical results by applying them to special cases and comparing them with relevant results in the literature.