Fourth-Order Neutral Differential Equation: A Modified Approach to Optimizing Monotonic Properties

Amany Nabih (), Osama Moaaz (), Sameh S. Askar, Ahmad M. Alshamrani and Elmetwally M. Elabbasy
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Amany Nabih: Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
Osama Moaaz: Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
Sameh S. Askar: Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
Ahmad M. Alshamrani: Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
Elmetwally M. Elabbasy: Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

Mathematics, 2023, vol. 11, issue 20, 1-15

Abstract: In this article, we investigate some qualitative properties of solutions to a class of functional differential equations with multi-delay. Using a modified approach, we first derive a number of optimized relations and inequalities that relate the solution x s to its corresponding function z s and its derivatives. After classifying the positive solutions, we follow the Riccati approach and principle of comparison, where fourth-order differential equations are compared with first-order differential equations to obtain conditions that exclude the positive solutions. Then, we introduce new oscillation conditions. With regard to previous relevant results, our results are an extension and complement to them. This work has theoretical significance in that it uncovers some new relationships that aid in developing the oscillation theory of higher-order equations in addition to the applied relevance of neutral differential equations.

Keywords: neutral differential equation; fourth order; monotonic properties; oscillation; canonical case (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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