(untitled) (European Journal of Pure and Applied Mathematics, 2025)
Our objective in this work is to establish new asymptotic and monotonic properties of second-order differential equations involving multiple delay terms and a damping component. These properties are instrumental in advancing the understanding of the qualitative behavior of their solutions. This study employs a refined comparison technique utilizing first-order differential equations. The resulting criteria broaden and enhance previously established findings in the literature. A natural progression and forthcoming challenge of this research is examining the oscillatory behavior and asymptotic characteristics of solutions for higher-order neutral delay differential equations, where the interplay between delay and neutral components becomes progressively intricate.