Second order neutral delay differential equations and their oscillatory criteria derived by linearization
Electronic Journal of Qualitative Theory of Differential Equations, vol.2025, 2025 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 2025
- Publication Date: 2025
- Doi Number: 10.14232/ejqtde.2025.1.45
- Journal Name: Electronic Journal of Qualitative Theory of Differential Equations
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Central & Eastern European Academic Source (CEEAS), zbMATH, Directory of Open Access Journals
- Keywords: second order neutral delay differential equations, asymptotic properties, linearization, oscillation theory
- Erciyes University Affiliated: Yes
Abstract
In this paper, we investigate the oscillatory behavior of second-order neutral delay differential equations with a canonical operator of the form (a(x)(v′ (x))m)′ + C(x, u(φ(x))) = 0. We introduce new monotonicity properties of the non-oscillatory solutions of these equations, which are then used to linearize the equations and derive new oscillatory criteria. The presented results significantly improve upon existing criteria.