On the Monotonic and Asymptotic Properties of Positive Solutions to Third-Order Neutral Differential Equations and Their Effect on Oscillation Criteria

On the Monotonic and Asymptotic Properties of Positive Solutions to Third-Order Neutral Differential Equations and Their Effect on Oscillation Criteria

The monotonic properties of positive solutions to functional differential equations of the third order are examined in this paper. It is generally known that by optimizing the relationships between a solution and its corresponding function, as well as its derivatives, one can improve the oscillation...

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Veröffentlicht in:Axioms 2023, Vol.12 (12)
Hauptverfasser: Essam, Amira, Moaaz, Osama, Ramadan, Moutaz, AlNemer, Ghada, Hanafy, Ibrahim M
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Sprache:eng
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Differential equations
Oscillation
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Moaaz, Osama
Ramadan, Moutaz
AlNemer, Ghada
Hanafy, Ibrahim M
description The monotonic properties of positive solutions to functional differential equations of the third order are examined in this paper. It is generally known that by optimizing the relationships between a solution and its corresponding function, as well as its derivatives, one can improve the oscillation criterion for neutral differential equations. Based on this, we obtain new relationships and inequalities and test their effect on the oscillation parameters of the studied equation. To obtain the oscillation parameters, we used Riccati techniques and comparison with lower-order equations. Finally, the progress achieved in oscillation theory for third-order equations was measured by comparing our results with previous relevant results.
doi_str_mv 10.3390/axioms12121086
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subjects Differential equations
Oscillation
title On the Monotonic and Asymptotic Properties of Positive Solutions to Third-Order Neutral Differential Equations and Their Effect on Oscillation Criteria
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