Oscillatory Analysis of Third-Order Hybrid Trinomial Delay Differential Equations Via Binomial Transform

This paper explores the oscillatory behavior of a class of third-order hybrid-type delay differential equations. A novel approach involves transforming these complex trinomial equations into a simpler binomial form by utilizing solutions from associated linear differential equations. Through the application of comparison techniques and integral averaging methods, new criteria are established that guarantee all solutions exhibit oscillatory behavior. These findings expand and complement existing theories in the oscillation analysis of functional differential equations. An illustrative example is provided to demonstrate the significance and originality of the results.