Nonlinear Neutral Delay Differential Equations: Novel Criteria for Oscillation and Asymptotic Behavior
This research deals with the study of the oscillatory behavior of solutions of second-order differential equations containing neutral conditions, both in sublinear and superlinear terms, with a focus on the noncanonical case. The research provides a careful analysis of the monotonic properties of so...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/13/1/147 |
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| author | Belal Batiha Nawa Alshammari Faten Aldosari Fahd Masood Omar Bazighifan |
| author_facet | Belal Batiha Nawa Alshammari Faten Aldosari Fahd Masood Omar Bazighifan |
| author_sort | Belal Batiha |
| collection | DOAJ |
| description | This research deals with the study of the oscillatory behavior of solutions of second-order differential equations containing neutral conditions, both in sublinear and superlinear terms, with a focus on the noncanonical case. The research provides a careful analysis of the monotonic properties of solutions and their derivatives, paving the way for a deeper understanding of this complex behavior. The research is particularly significant as it extends the scope of previous studies by addressing more complex forms of neutral differential equations. Using the linearization technique, strict conditions are developed that exclude the existence of positive solutions, which allows the formulation of innovative criteria for determining the oscillatory behavior of the studied equations. This research highlights the theoretical and applied aspects of this mathematical phenomenon, which contributes to enhancing the scientific understanding of differential equations with neutral conditions. To demonstrate the effectiveness of the results, the research includes two illustrative examples that prove the validity and importance of the proposed methodology. This work represents a qualitative addition to the mathematical literature, as it lays new foundations and opens horizons for future studies in this vital field. |
| format | Article |
| id | doaj-art-6a6ec978af6e47eca1c27a7979350329 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-6a6ec978af6e47eca1c27a79793503292025-01-10T13:18:24ZengMDPI AGMathematics2227-73902025-01-0113114710.3390/math13010147Nonlinear Neutral Delay Differential Equations: Novel Criteria for Oscillation and Asymptotic BehaviorBelal Batiha0Nawa Alshammari1Faten Aldosari2Fahd Masood3Omar Bazighifan4Mathematics Department, Faculty of Science and Information Technology, Jadara University, Irbid 21110, JordanDepartment of Basic Sciences, College of Science and Theoretical Studies, Saudi Electronic University, Riyadh 11673, Saudi ArabiaDepartment of Mathematics, College of Science, Shaqra University, P.O. Box 15572, Shaqra 11961, Saudi ArabiaDepartment of Mathematics, Faculty of Education and Science, University of Saba Region, Marib 14400, YemenDepartment of Mathematics, Faculty of Education, Seiyun University, Seiyun 50512, YemenThis research deals with the study of the oscillatory behavior of solutions of second-order differential equations containing neutral conditions, both in sublinear and superlinear terms, with a focus on the noncanonical case. The research provides a careful analysis of the monotonic properties of solutions and their derivatives, paving the way for a deeper understanding of this complex behavior. The research is particularly significant as it extends the scope of previous studies by addressing more complex forms of neutral differential equations. Using the linearization technique, strict conditions are developed that exclude the existence of positive solutions, which allows the formulation of innovative criteria for determining the oscillatory behavior of the studied equations. This research highlights the theoretical and applied aspects of this mathematical phenomenon, which contributes to enhancing the scientific understanding of differential equations with neutral conditions. To demonstrate the effectiveness of the results, the research includes two illustrative examples that prove the validity and importance of the proposed methodology. This work represents a qualitative addition to the mathematical literature, as it lays new foundations and opens horizons for future studies in this vital field.https://www.mdpi.com/2227-7390/13/1/147oscillationnon-oscillationsublinear typesuperlinear typeneutral differential equationsecond order |
| spellingShingle | Belal Batiha Nawa Alshammari Faten Aldosari Fahd Masood Omar Bazighifan Nonlinear Neutral Delay Differential Equations: Novel Criteria for Oscillation and Asymptotic Behavior Mathematics oscillation non-oscillation sublinear type superlinear type neutral differential equation second order |
| title | Nonlinear Neutral Delay Differential Equations: Novel Criteria for Oscillation and Asymptotic Behavior |
| title_full | Nonlinear Neutral Delay Differential Equations: Novel Criteria for Oscillation and Asymptotic Behavior |
| title_fullStr | Nonlinear Neutral Delay Differential Equations: Novel Criteria for Oscillation and Asymptotic Behavior |
| title_full_unstemmed | Nonlinear Neutral Delay Differential Equations: Novel Criteria for Oscillation and Asymptotic Behavior |
| title_short | Nonlinear Neutral Delay Differential Equations: Novel Criteria for Oscillation and Asymptotic Behavior |
| title_sort | nonlinear neutral delay differential equations novel criteria for oscillation and asymptotic behavior |
| topic | oscillation non-oscillation sublinear type superlinear type neutral differential equation second order |
| url | https://www.mdpi.com/2227-7390/13/1/147 |
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