Properties of second order differential equations with advanced and delay argument

In this paper, we study the second-order linear delay differential equation of the form y ''(t) +p(t)y(tau(t)) = 0. (E) We establish new oscillation criteria for (E), which improve a number of related ones in the literature. Our approach essentially involves establishing stronger monotonicity properties for the positive solutions of (E) than those presented in known works. Two main approaches for the investigation of (E) will be used, namely a comparison principle with first-order delay differential inequalities and generalization of very effective Koplatadze's technique. We illustrate the improvement over the known results by applying and comparing our method with the other known results for (E). (c) 2023 Elsevier Ltd. All rights reserved.