Asymptotic and Oscillatory Behaviour of Third Order Non-linear Differential Equations with Canonical Operator and Mixed Neutral Terms

This paper deals with the asymptotic and oscillatory behaviour of third-order non-linear differential equations with mixed non-linear neutral terms and a canonical operator. The results are obtained via utilising integral conditions as well as comparison theorems with the oscillatory properties of first-order advanced and/or delay differential equations. The proposed theorems improve, extend, and simplify existing ones in the literature. The results are illustrated by two numerical examples.