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Oscillation Theory for Non-Linear Neutral Delay Differential Equations of Third Order
Article

Oscillatory Properties of Odd-Order Delay Differential Equations with Distribution Deviating Arguments

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Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
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Department of Mathematics, Faculty of Education—Al-Nadirah, Ibb University, Ibb P.O. Box 70270, Yemen
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Department of Mathematics and General Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
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Department of Medical Research, China Medical University, Taichung 40402, Taiwan
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Department of Computer Science and Information Engineering, Asia University, Taichung 40402, Taiwan
*
Authors to whom correspondence should be addressed.
Appl. Sci. 2020, 10(17), 5952; https://doi.org/10.3390/app10175952
Received: 28 June 2020 / Revised: 25 August 2020 / Accepted: 26 August 2020 / Published: 27 August 2020
Throughout this work, new criteria for the asymptotic behavior and oscillation of a class of odd-order delay differential equations with distributed deviating arguments are established. Our method is essentially based on establishing sharper estimates for positive solutions of the studied equation, using an iterative technique. Moreover, the iterative technique allows us to test the oscillation, even when the related results fail to apply. By establishing new comparison theorems that compare the nth-order equations with one or a couple of first-order delay differential equations, we obtain new conditions for oscillation of all solutions of the studied equation. To show the importance of our results, we provide two examples. View Full-Text
Keywords: positive solutions; delay differential equations; odd-order positive solutions; delay differential equations; odd-order
MDPI and ACS Style

Muhib, A.; Abdeljawad, T.; Moaaz, O.; Elabbasy, E.M. Oscillatory Properties of Odd-Order Delay Differential Equations with Distribution Deviating Arguments. Appl. Sci. 2020, 10, 5952. https://doi.org/10.3390/app10175952

AMA Style

Muhib A, Abdeljawad T, Moaaz O, Elabbasy EM. Oscillatory Properties of Odd-Order Delay Differential Equations with Distribution Deviating Arguments. Applied Sciences. 2020; 10(17):5952. https://doi.org/10.3390/app10175952

Chicago/Turabian Style

Muhib, Ali, Thabet Abdeljawad, Osama Moaaz, and Elmetwally M. Elabbasy. 2020. "Oscillatory Properties of Odd-Order Delay Differential Equations with Distribution Deviating Arguments" Applied Sciences 10, no. 17: 5952. https://doi.org/10.3390/app10175952

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