Oscillation Criteria for a Class of Fourth-Order Nonlinear Neutral Delay Differential Equations

Abstract

The oscillatory characteristics of solutions for a class of nonlinear fourth-order neutral delay differential equations are the primary focus of this work. By extending previously established results, we derive new sufficient conditions that guarantee oscillation. These conditions are developed using advanced analytical tools, including Riccati transformations, comparison principles, and integral inequalities. The neutral nature and high order of the equations considered add complexity, particularly due to the delayed terms appearing in both the dependent variable and its derivatives. Several lemmas and theorems are established to support the main results, an example is provided to illustrate the validity and applicability of the obtained criteria. These results significantly generalize upon known oscillation criteria for fourth-order neutral delay differential equations.