New improved results for oscillation of fourth-order neutral differential equations

Abstract

In this study, a new oscillation criterion for the fourth-order neutral delay differential equation r(u) (x(u) + p(u)x(δ(u)))′′′) α) ′ ( ( + q(u)xβ (φ(u)) = 0, u ≥ u0 is established. By introducing a Riccati substitution, we obtain a new criterion for oscillation without requiring the existence of the unknown function. Furthermore, the new criterion improves and complements the previous results in the literature. The results obtained are illustrated by an example.