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)y0(t)α0+q(t)yα(τ(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.