New criteria for the oscillation of a class of third-order quasilinear delay differential equations

This paper establishes new criteria for the oscillation of solutions to a specific class of third-order delay differential equations. These equations, which have numerous applications in the physical and biological sciences, pose intriguing analytical challenges. By employing novel ordering properties, the comparison principle, Riccati transformations, and other analytical techniques, we derive effective oscillation criteria. This approach addresses and overcomes several restrictions previously imposed on the coefficients of such equations. To demonstrate the novelty and practical relevance of our results, we include illustrative examples.