Investigation of the Oscillatory Behavior of the Solutions of a Class of Third-Order Delay Differential Equations with Several Terms

Abstract

In this paper, we address the study of the oscillatory properties of the solutions of a class of third-order delay differential equations. The primary objective of this study is to provide new relationships that can be employed to obtain criteria for excluding increasing positive solutions and decreasing positive solutions so that the resulting criteria are easier to apply than other criteria that have appeared in the literature. We have obtained new oscillation criteria that hold up more robustly upon application. Some examples are presented to illustrate the significance of our main findings.

Keywords

• third-order differential equation
• oscillation
• nonoscillation
• delay