Fourth-Order Emden–Fowler Neutral Differential Equations: Investigating Some Qualitative Properties of Solutions

In this article, we investigate some of the qualitative properties of a class of fourth-order neutral differential equations. We start by obtaining new inequalities and relations between the solution and its corresponding function, as well as with its derivatives. The new relations allow us to impro...

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Bibliographic Details
Published in:Symmetry (Basel) 2023-07, Vol.15 (7), p.1446
Main Authors: Alatwi, Mansour, Moaaz, Osama, Askar, Sameh S., Alshamrani, Ahmad M., Elabbasy, Elmetwally M.
Format: Article
Language:English
Subjects:
Asymptotic properties
Control theory
Criteria
Differential equations
Engineering
fourth order
Mathematical analysis
neutral differential equation
non-oscillatory
oscillatory
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Summary:In this article, we investigate some of the qualitative properties of a class of fourth-order neutral differential equations. We start by obtaining new inequalities and relations between the solution and its corresponding function, as well as with its derivatives. The new relations allow us to improve the monotonic and asymptotic properties of the positive solutions of the studied equation. Then, using an improved approach, we establish new criteria that test the oscillation of all solutions. We also rely on the principle of symmetry between positive and negative solutions to obtain the new criteria. The paper provides illustrative examples that highlight the significance of our findings.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym15071446