New Improved Results for Oscillation of Fourth-Order Neutral Differential Equations - Osama Moaaz; Rami Ahmad El-Nabulsi; Ali Muhib; Sayed K. Elagan; Mohammed Zakarya (Mathematics, 2021)
In this study, a new oscillation criterion for the fourth-order neutral delay differential equation <semantics><mfenced separators="" open="(" close=")">r<mfenced open="(" close=")">u</mfenced><mfenced separators="" open="(" close=")"><mfenced separators="" open="(" close=")">x<mfenced open="(" close=")">u</mfenced>+p<mfenced open="(" close=")">u</mfenced>x<mfenced separators="" open="(" close=")">δ<mfenced open="(" close=")">u</mfenced></mfenced></mfenced>‴</mfenced>α</mfenced>′+q<mfenced open="(" close=")">u</mfenced>xβ<mfenced separators="" open="(" close=")">ϕ<mfenced open="(" close=")">u</mfenced></mfenced>=0,<mspace width="4.pt"></mspace>u≥u0</semantics> 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.