Second order neutral delay differential equations and their oscillatory criteria derived by linearization

TEMTEK P., Turarov Y.

Electronic Journal of Qualitative Theory of Differential Equations, cilt.2025, 2025 (SCI-Expanded, Scopus) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 2025
  • Basım Tarihi: 2025
  • Doi Numarası: 10.14232/ejqtde.2025.1.45
  • Dergi Adı: Electronic Journal of Qualitative Theory of Differential Equations
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Central & Eastern European Academic Source (CEEAS), zbMATH, Directory of Open Access Journals
  • Anahtar Kelimeler: second order neutral delay differential equations, asymptotic properties, linearization, oscillation theory
  • Erciyes Üniversitesi Adresli: Evet

Özet

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.