Existence of Oscillatory Solutions for Second‐Order Functional Differential Equations With Time Delay

This paper investigates the existence of oscillatory behavior of solutions for the following second‐order delay differential equation By using the Schauder–Tychonoff fixed‐point theorem and Ascoli–Arzelà theorem, sufficient conditions for the existence of oscillatory solutions are derived. Some illustrative examples and numerical simulations are presented to demonstrate the validity of our results. The results of this study further complete the general understanding of dynamic systems and may be of potential applicability in many scientific and engineering disciplines where oscillations are essential.