Improved Oscillation Theorems for Even-Order Quasi-Linear Neutral Differential Equations
In this study, our goal was to establish improved inequalities that enhance the asymptotic and oscillatory behaviors of solutions to even-order neutral differential equations. In the oscillation theory of neutral differential equations, the connection between the solution and its corresponding funct...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-05-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/5/1128 |
| _version_ | 1797598249013477376 |
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| author | Yousef Alnafisah Fahd Masood Ali Muhib Osama Moaaz |
| author_facet | Yousef Alnafisah Fahd Masood Ali Muhib Osama Moaaz |
| author_sort | Yousef Alnafisah |
| collection | DOAJ |
| description | In this study, our goal was to establish improved inequalities that enhance the asymptotic and oscillatory behaviors of solutions to even-order neutral differential equations. In the oscillation theory of neutral differential equations, the connection between the solution and its corresponding function plays a critical role. We refined these relationships by leveraging the modified monotonic properties of positive solutions and introduced new conditions that ensure the absence of positive solutions, confirming the oscillation of all solutions to the studied equation. Based on the concept of symmetry between the positive and negative solutions of the studied equation, we obtained criteria that guarantee the oscillation of all solutions by excluding positive solutions only. In order to demonstrate the significance of our findings, we examined certain instances of the studied equation and compared them with previous results in the literature. |
| first_indexed | 2024-03-11T03:16:39Z |
| format | Article |
| id | doaj.art-b59dd6b917ef49c99f9ce32a08575156 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-11T03:16:39Z |
| publishDate | 2023-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-b59dd6b917ef49c99f9ce32a085751562023-11-18T03:31:19ZengMDPI AGSymmetry2073-89942023-05-01155112810.3390/sym15051128Improved Oscillation Theorems for Even-Order Quasi-Linear Neutral Differential EquationsYousef Alnafisah0Fahd Masood1Ali Muhib2Osama Moaaz3Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, EgyptDepartment of Mathematics, Faculty of Education—Al-Nadirah, Ibb University, Ibb 70270, YemenDepartment of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi ArabiaIn this study, our goal was to establish improved inequalities that enhance the asymptotic and oscillatory behaviors of solutions to even-order neutral differential equations. In the oscillation theory of neutral differential equations, the connection between the solution and its corresponding function plays a critical role. We refined these relationships by leveraging the modified monotonic properties of positive solutions and introduced new conditions that ensure the absence of positive solutions, confirming the oscillation of all solutions to the studied equation. Based on the concept of symmetry between the positive and negative solutions of the studied equation, we obtained criteria that guarantee the oscillation of all solutions by excluding positive solutions only. In order to demonstrate the significance of our findings, we examined certain instances of the studied equation and compared them with previous results in the literature.https://www.mdpi.com/2073-8994/15/5/1128neutral differential equationsoscillatory propertieseven-order differential equation |
| spellingShingle | Yousef Alnafisah Fahd Masood Ali Muhib Osama Moaaz Improved Oscillation Theorems for Even-Order Quasi-Linear Neutral Differential Equations Symmetry neutral differential equations oscillatory properties even-order differential equation |
| title | Improved Oscillation Theorems for Even-Order Quasi-Linear Neutral Differential Equations |
| title_full | Improved Oscillation Theorems for Even-Order Quasi-Linear Neutral Differential Equations |
| title_fullStr | Improved Oscillation Theorems for Even-Order Quasi-Linear Neutral Differential Equations |
| title_full_unstemmed | Improved Oscillation Theorems for Even-Order Quasi-Linear Neutral Differential Equations |
| title_short | Improved Oscillation Theorems for Even-Order Quasi-Linear Neutral Differential Equations |
| title_sort | improved oscillation theorems for even order quasi linear neutral differential equations |
| topic | neutral differential equations oscillatory properties even-order differential equation |
| url | https://www.mdpi.com/2073-8994/15/5/1128 |
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