Fourth-order differential equations with neutral delay: Investigation of monotonic and oscillatory features
For fourth-order neutral differential equations (NDE) in the canonical case, we present new relationships between the solution and its corresponding function in two casses: $ p < 1 $ and $ p > 1 $. Through these relationships, we discover new monotonic properties for this equation of fourth or...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-12-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241630 |
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| author | H. Salah M. Anis C. Cesarano S. S. Askar A. M. Alshamrani E. M. Elabbasy |
| author_facet | H. Salah M. Anis C. Cesarano S. S. Askar A. M. Alshamrani E. M. Elabbasy |
| author_sort | H. Salah |
| collection | DOAJ |
| description | For fourth-order neutral differential equations (NDE) in the canonical case, we present new relationships between the solution and its corresponding function in two casses: $ p < 1 $ and $ p > 1 $. Through these relationships, we discover new monotonic properties for this equation of fourth order. Using the new relationships and properties, we derive some oscillation conditions for the equation under study. By using the Comparison and Ricatti technique, the positive solutions are excluded by providing some conditions. Lastly, we provide examples and review previous theorems from the literature to compare our findings. |
| format | Article |
| id | doaj-art-decc960fbc324fc3bcd6af579f561ef2 |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-decc960fbc324fc3bcd6af579f561ef22025-01-23T07:53:25ZengAIMS PressAIMS Mathematics2473-69882024-12-01912342243424710.3934/math.20241630Fourth-order differential equations with neutral delay: Investigation of monotonic and oscillatory featuresH. Salah0M. Anis1C. Cesarano2S. S. Askar3A. M. Alshamrani4E. M. Elabbasy5Department of Mathematics, Faculty of Science, Mansoura University, 35516 Mansoura, EgyptDepartment of Mathematics, Faculty of Science, Mansoura University, 35516 Mansoura, EgyptSection of Mathematics, International Telematic University Uninettuno, CorsoVittorio Emanuele Ⅱ, 39, 00186 Roma, ItalyDepartment 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, 35516 Mansoura, EgyptFor fourth-order neutral differential equations (NDE) in the canonical case, we present new relationships between the solution and its corresponding function in two casses: $ p < 1 $ and $ p > 1 $. Through these relationships, we discover new monotonic properties for this equation of fourth order. Using the new relationships and properties, we derive some oscillation conditions for the equation under study. By using the Comparison and Ricatti technique, the positive solutions are excluded by providing some conditions. Lastly, we provide examples and review previous theorems from the literature to compare our findings.https://www.aimspress.com/article/doi/10.3934/math.20241630functional differential equationneutraloscillationfourth-ordercanonical |
| spellingShingle | H. Salah M. Anis C. Cesarano S. S. Askar A. M. Alshamrani E. M. Elabbasy Fourth-order differential equations with neutral delay: Investigation of monotonic and oscillatory features AIMS Mathematics functional differential equation neutral oscillation fourth-order canonical |
| title | Fourth-order differential equations with neutral delay: Investigation of monotonic and oscillatory features |
| title_full | Fourth-order differential equations with neutral delay: Investigation of monotonic and oscillatory features |
| title_fullStr | Fourth-order differential equations with neutral delay: Investigation of monotonic and oscillatory features |
| title_full_unstemmed | Fourth-order differential equations with neutral delay: Investigation of monotonic and oscillatory features |
| title_short | Fourth-order differential equations with neutral delay: Investigation of monotonic and oscillatory features |
| title_sort | fourth order differential equations with neutral delay investigation of monotonic and oscillatory features |
| topic | functional differential equation neutral oscillation fourth-order canonical |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241630 |
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