More Effective Criteria for Testing the Asymptotic and Oscillatory Behavior of Solutions of a Class of Third-Order Functional Differential Equations
This paper delves into the investigation of quasi-linear neutral differential equations in the third-order canonical case. In this study, we refine the relationship between the solution and its corresponding function, leading to improved preliminary results. These enhanced results play a crucial rol...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-12-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/12/1112 |
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| author | Fahd Masood Osama Moaaz Ghada AlNemer Hamdy El-Metwally |
| author_facet | Fahd Masood Osama Moaaz Ghada AlNemer Hamdy El-Metwally |
| author_sort | Fahd Masood |
| collection | DOAJ |
| description | This paper delves into the investigation of quasi-linear neutral differential equations in the third-order canonical case. In this study, we refine the relationship between the solution and its corresponding function, leading to improved preliminary results. These enhanced results play a crucial role in excluding the existence of positive solutions to the investigated equation. By building upon the improved preliminary results, we introduce novel criteria that shed light on the nature of these solutions. These criteria help to distinguish whether the solutions exhibit oscillatory behavior or tend toward zero. Moreover, we present oscillation criteria for all solutions. To demonstrate the relevance of our results, we present an illustrative example. This example validates the theoretical framework we have developed and offers practical insights into the behavior of solutions for quasi-linear third-order neutral differential equations. |
| first_indexed | 2024-03-08T20:59:45Z |
| format | Article |
| id | doaj.art-712743536dc44522b5529f52f148b5d9 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-08T20:59:45Z |
| publishDate | 2023-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-712743536dc44522b5529f52f148b5d92023-12-22T13:53:16ZengMDPI AGAxioms2075-16802023-12-011212111210.3390/axioms12121112More Effective Criteria for Testing the Asymptotic and Oscillatory Behavior of Solutions of a Class of Third-Order Functional Differential EquationsFahd Masood0Osama Moaaz1Ghada AlNemer2Hamdy El-Metwally3Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, EgyptDepartment of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi ArabiaDepartment of Mathematical Science, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 105862, Riyadh 11656, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, EgyptThis paper delves into the investigation of quasi-linear neutral differential equations in the third-order canonical case. In this study, we refine the relationship between the solution and its corresponding function, leading to improved preliminary results. These enhanced results play a crucial role in excluding the existence of positive solutions to the investigated equation. By building upon the improved preliminary results, we introduce novel criteria that shed light on the nature of these solutions. These criteria help to distinguish whether the solutions exhibit oscillatory behavior or tend toward zero. Moreover, we present oscillation criteria for all solutions. To demonstrate the relevance of our results, we present an illustrative example. This example validates the theoretical framework we have developed and offers practical insights into the behavior of solutions for quasi-linear third-order neutral differential equations.https://www.mdpi.com/2075-1680/12/12/1112oscillatorynonoscillatorydelay differential equationthird-ordercanonical |
| spellingShingle | Fahd Masood Osama Moaaz Ghada AlNemer Hamdy El-Metwally More Effective Criteria for Testing the Asymptotic and Oscillatory Behavior of Solutions of a Class of Third-Order Functional Differential Equations Axioms oscillatory nonoscillatory delay differential equation third-order canonical |
| title | More Effective Criteria for Testing the Asymptotic and Oscillatory Behavior of Solutions of a Class of Third-Order Functional Differential Equations |
| title_full | More Effective Criteria for Testing the Asymptotic and Oscillatory Behavior of Solutions of a Class of Third-Order Functional Differential Equations |
| title_fullStr | More Effective Criteria for Testing the Asymptotic and Oscillatory Behavior of Solutions of a Class of Third-Order Functional Differential Equations |
| title_full_unstemmed | More Effective Criteria for Testing the Asymptotic and Oscillatory Behavior of Solutions of a Class of Third-Order Functional Differential Equations |
| title_short | More Effective Criteria for Testing the Asymptotic and Oscillatory Behavior of Solutions of a Class of Third-Order Functional Differential Equations |
| title_sort | more effective criteria for testing the asymptotic and oscillatory behavior of solutions of a class of third order functional differential equations |
| topic | oscillatory nonoscillatory delay differential equation third-order canonical |
| url | https://www.mdpi.com/2075-1680/12/12/1112 |
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