New Improved Results for Oscillation of Fourth-Order Neutral Differential Equations

Mathematics

Sayed K. Elagan¹  Mohammed Zakarya²  Ali Muhib³  Osama Moaaz³  Rami Ahmad El-Nabulsi⁴ 

[1] Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia;Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia;Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt;Research Center for Quantum Technology, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand;

关键词: delay differential equation;    neutral;    oscillation;    fourth-order;   

DOI  :  10.3390/math9192388

来源: DOAJ

【 摘 要 】

In this study, a new oscillation criterion for the fourth-order neutral delay differential equation ${\left(r\left(u\right){\left({\left(x\left(u\right)+p\left(u\right)x\left(\delta \left(u\right)\right)\right)}^{‴}\right)}^{\alpha }\right)}^{\prime }+q\left(u\right)x^{\beta }\left(\varphi \left(u\right)\right)=0,u\ge u_0$ 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.

【 授权许可】

Unknown