Delay Differential Equations with Several Sublinear Neutral Terms: Investigation of Oscillatory Behavior

Abstract

In this work, new oscillation criteria are established for a second-order differential equation with several sublinear neutral terms and in the canonical case. To determine the oscillation conditions, we followed the Riccati approach and also compared the studied equation with a first-order delay equation. Obtaining the oscillation conditions required deducing some new relationships linking the solution to the corresponding function as well as its derivatives. The paper addresses some interesting analytical points in the study of the oscillation of equations with several sublinear neutral terms. These new findings complement some well-known findings in the literature. Furthermore, an example is provided to show the importance of the results.

Keywords

• functional differential equation
• second order
• several sublinear neutral terms
• oscillatory behavior
• Riccati approach
• comparison principles