Functional Differential Equations with an Advanced Neutral Term: New Monotonic Properties of Recursive Nature to Optimize Oscillation Criteria

The goal of this study is to derive new conditions that improve the testing of the oscillatory and asymptotic features of fourth-order differential equations with an advanced neutral term. By using Riccati techniques and comparison with lower-order equations, we establish new criteria that verify th...

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Bibliographic Details
Published in:Axioms 2024-12, Vol.13 (12), p.847
Main Authors: Nabih, Amany, Albalawi, Wedad, Jazmati, Mohammad S, Elrashidi, Ali, Ali, Hegagi M, Moaaz, Osama
Format: Article
Language:English
Subjects:
advanced neutral term
Agarwal, Ravi P
Analysis
Control engineering
Criteria
differential equation
Differential equations
fourth-order functional equations
Mathematical functions
Mathematical models
Ordinary differential equations
oscillation theorems
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Summary:The goal of this study is to derive new conditions that improve the testing of the oscillatory and asymptotic features of fourth-order differential equations with an advanced neutral term. By using Riccati techniques and comparison with lower-order equations, we establish new criteria that verify the absence of positive solutions and, consequently, the oscillation of all solutions to the investigated equation. Using our results to analyze a few specific instances of the examined equation, we can ultimately clarify the significance of the new inequalities. Our results are an extension of previous results that considered equations with a neutral delay term and also an improvement of previous results that considered only equations with an advanced neutral term.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms13120847