High-Order Nonlinear Functional Differential Equations: New Monotonic Properties and Their Applications

Abstract

We provide streamlined criteria for evaluating the oscillatory behavior of solutions to a class of higher-order functional differential equations in the non-canonical case. We use a comparison approach with first-order equations that have standard oscillation criteria. Normally, in the non-canonical situation, the oscillation test requires three independent conditions, but we provide criteria with two-conditions without checking the additional conditions. Lastly, we give examples to highlight the significance of the findings.

Keywords

• functional differential equations
• delay
• higher-order
• oscillatory
• non-canonical case