Improved oscillation results for second-order half-linear delay differential equations

Abstract

In this paper, we study the second-order half-linear delay differential equation of the form\[(r(t)(y'(t))^\alpha)'+q(t)y^\alpha(\tau(t))= 0.\:\:\:(E)\]We establish new oscillation criteria for (E), which improve a number of related ones in the literature. Our approach essentially involves establishing sharper estimates for the positive solutions of (E) than those presented in known works and a comparison principle with first-order delay differential inequalities. We illustrate the improvement over the known results by applying and comparing our method with the other known methods on the particular example of Euler-type equations.