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

• Published in: Qualitative theory of dynamical systems Vol. 22; no. 1
• Main Authors: Alzabut, J., Grace, S. R., Santra, S. S., Chhatria, G. N.
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.03.2023; Springer Nature B.V
• Subjects: Asymptotic properties; Difference and Functional Equations; Dynamical Systems and Ergodic Theory; Mathematical analysis; Mathematics; Mathematics and Statistics; Nonlinear differential equations; Operators (mathematics); Theorems; Mixed neutral terms; Non-linear differential equations; Canonical operator; 34N05; Oscillation; Asymptotic behavior; 34K11
• ISSN: 1575-5460; 1662-3592
• DOI: 10.1007/s12346-022-00715-6

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.