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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| Format: | Article |
| Language: | English |
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MDPI AG
2023-07-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/7/1446 |
| _version_ | 1797587415367417856 |
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| author | Mansour Alatwi Osama Moaaz Sameh S. Askar Ahmad M. Alshamrani Elmetwally M. Elabbasy |
| author_facet | Mansour Alatwi Osama Moaaz Sameh S. Askar Ahmad M. Alshamrani Elmetwally M. Elabbasy |
| author_sort | Mansour Alatwi |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-11T00:36:40Z |
| format | Article |
| id | doaj.art-ec3275ce55c6439b97bb57c55c1bd335 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-11T00:36:40Z |
| publishDate | 2023-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-ec3275ce55c6439b97bb57c55c1bd3352023-11-18T21:35:09ZengMDPI AGSymmetry2073-89942023-07-01157144610.3390/sym15071446Fourth-Order Emden–Fowler Neutral Differential Equations: Investigating Some Qualitative Properties of SolutionsMansour Alatwi0Osama Moaaz1Sameh S. Askar2Ahmad M. Alshamrani3Elmetwally M. Elabbasy4Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, EgyptDepartment of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, EgyptDepartment of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaDepartment of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, EgyptIn 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.https://www.mdpi.com/2073-8994/15/7/1446oscillatorynon-oscillatoryneutral differential equationfourth order |
| spellingShingle | Mansour Alatwi Osama Moaaz Sameh S. Askar Ahmad M. Alshamrani Elmetwally M. Elabbasy Fourth-Order Emden–Fowler Neutral Differential Equations: Investigating Some Qualitative Properties of Solutions Symmetry oscillatory non-oscillatory neutral differential equation fourth order |
| title | Fourth-Order Emden–Fowler Neutral Differential Equations: Investigating Some Qualitative Properties of Solutions |
| title_full | Fourth-Order Emden–Fowler Neutral Differential Equations: Investigating Some Qualitative Properties of Solutions |
| title_fullStr | Fourth-Order Emden–Fowler Neutral Differential Equations: Investigating Some Qualitative Properties of Solutions |
| title_full_unstemmed | Fourth-Order Emden–Fowler Neutral Differential Equations: Investigating Some Qualitative Properties of Solutions |
| title_short | Fourth-Order Emden–Fowler Neutral Differential Equations: Investigating Some Qualitative Properties of Solutions |
| title_sort | fourth order emden fowler neutral differential equations investigating some qualitative properties of solutions |
| topic | oscillatory non-oscillatory neutral differential equation fourth order |
| url | https://www.mdpi.com/2073-8994/15/7/1446 |
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