Refined monotonicity-based approach to oscillation in second-order half-linear delay differential equations

Abstract

This study aims to establish advanced oscillation criteria for second-order half-linear delay differential equations, thus broadening the existing theoretical framework. Our method relies on establishing stronger monotonicity properties for the solutions than those previously available. We employ a primary approach in our analysis: a comparison principle involving first-order delay differential inequalities. An illustrative example is presented to demonstrate the superiority of the proposed method compared to existing results.