Third-Order Functional Differential Equations with Damping Term: Oscillatory Behavior of Solutions

In this paper, we investigate the asymptotic and oscillatory behavior of a specific class of third-order functional differential equations with damping terms and deviating arguments. By employing the comparison principle, Riccati transformation, and the integral averaging technique, we derive new criteria that guarantee all solutions to the studied equation oscillate when ${\int }_{{\top }_0}^{\infty }1/{\gamma }^{1/\alpha }\left(\top \right)\mathrm{d}\top =\infty$ and $\varrho \left(\top \right)\le {\varrho }_0<\infty$. This study introduces novel conditions and effective analytical tools, which enhance our understanding of such equations and broaden their range of applications. Illustrative examples are provided to demonstrate the applicability of the results.