Nonlinear oscillation analysis of delay differential equations with mixed neutral terms

This paper investigates novel sufficient conditions for the oscillatory behavior of fourth-order nonlinear differential equations with mixed neutral terms. By employing refined Riccati transformation techniques and advanced analytical approaches, we establish extended criteria that enrich the theoretical understanding of oscillation phenomena within this class of neutral differential equations. The proposed results significantly improve upon previously known conditions in the literature. Moreover, illustrative numerical examples are provided to demonstrate the applicability and sharpness of the obtained criteria. The findings contribute to the broader framework of nonlinear analysis and offer valuable insights into the oscillatory dynamics of functional differential equations with delay and neutral terms.