More Effective Conditions for Testing the Oscillatory Behavior of Solutions to a Class of Fourth-Order Functional Differential Equations

Abstract

This paper presents an investigation into the qualitative behavior of solutions for a specific class of fourth-order half-linear neutral differential equations. The main objective of this study is to improve the relationship between the solution and its corresponding function. By developing improved relationships, a novel criterion is proposed to determine the oscillatory behavior of the studied equation. The exclusion of positive solutions is achieved through a comparative approach in which the examined equation is compared to second-order equations. Additionally, the significance of the obtained results is demonstrated by applying them to various illustrative examples.

Keywords

• oscillatory
• non-oscillatory
• neutral differential equation
• fourth-order