New oscillation criteria for third-order functional differential equations with general delay argument

This study explores the asymptotic and oscillatory behavior of solutions to third-order functional differential equations. By employing Riccati transformation, we effectively eliminate the possibility of nonoscillatory solutions, allowing for the development of oscillation criteria that are applicable to a broad range of equation models. A key objective of this work is to relax traditional constraints commonly imposed on these criteria, thereby enhancing their general applicability. The results presented not only refine and extend existing theories but also contribute to a deeper understanding of the subject. Practical implications of the theoretical findings are demonstrated through several illustrative examples, highlighting their relevance and potential applications.