Oscillation Solutions for Nonlinear Second-Order Neutral Differential Equations

Abstract

This research investigates the oscillation criteria of nonlinear second-order neutral differential equations with multiple delays, focusing on their noncanonical forms. By leveraging an innovative iterative technique, new relationships are established to enhance the monotonic properties of positive solutions. These advancements lead to the derivation of novel oscillation criteria that significantly extend and refine the existing body of knowledge in this domain. The proposed criteria address gaps in the literature, providing a robust framework for analyzing such differential equations. To demonstrate their practical implications, three illustrative examples are presented, showcasing the applicability and effectiveness of the results in solving real-world problems involving delay differential equations.

Keywords

• oscillation criteria
• neutral differential equations
• multiple delays
• noncanonical forms