Oscillatory dynamics and recursive monotonicity of positive solutions to second-order neutral delay differential equations: Analytical framework and applications

This paper studies the oscillatory behavior of a class of second-order neutral delay differential equations (NDDEs). Using comparison principles and Riccati transformation techniques, we derived new sufficient conditions for oscillation. A recursive framework was introduced to enhance the monotonic properties of positive solutions, leading to sharper criteria. Auxiliary inequalities, exponential estimates, and integral averaging methods support the analysis. Illustrative examples demonstrate the applicability and improvements over existing results, positioning our findings within a broader context relevant to engineering and biological models.