Oscillatory Properties of Second-Order Differential Equations with Advanced Arguments in the Noncanonical Case

Abstract

This paper focuses on studying certain oscillatory properties of a new class of half-linear second-order differential equations with an advanced argument in a non-canonical case. By employing some new relations between the solution and its higher derivatives and taking into account the symmetry of positive and negative solutions, we have introduced new criteria to test whether all solutions of the studied equation exhibit oscillatory behavior. Our study aims to expand and enhance previous results, helping to understand these properties in the specified context. The results obtained are confirmed and clarified through an example involving Euler-type equations.

Keywords

• third-order differential equation
• oscillation
• nonoscillation
• delay