On the oscillation of fourth-order canonical differential equation with several delays

Abstract

This study is concerned with investigating the oscillatory properties of a general class of neutral differential equations. Neutral equations are characterized by being rich in both practical and theoretical aspects. We obtain criteria that guarantee the oscillation of solutions to a fourth-order neutral differential equation with multiple delays. Considering the canonical case, we obtain some new relations and inequalities that help in obtaining improved criteria. We use the reduction method to relate the oscillation of the studied equation to a first-order equation. We apply the results to a special case. Through this application, we evaluated the efficiency of the new results in the oscillation test compared to previous results in the literature.

Keywords

• canonical form
• fourth-order
• oscillation criteria