New Results for Oscillatory Behavior of Fourth-Order Differential Equations
Our aim in the present paper is to employ the Riccatti transformation which differs from those reported in some literature and comparison principles with the second-order differential equations, to establish some new conditions for the oscillation of all solutions of fourth-order differential equati...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-01-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/12/1/136 |
| _version_ | 1818035139356131328 |
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| author | Rami Ahmad El-Nabulsi Osama Moaaz Omar Bazighifan |
| author_facet | Rami Ahmad El-Nabulsi Osama Moaaz Omar Bazighifan |
| author_sort | Rami Ahmad El-Nabulsi |
| collection | DOAJ |
| description | Our aim in the present paper is to employ the Riccatti transformation which differs from those reported in some literature and comparison principles with the second-order differential equations, to establish some new conditions for the oscillation of all solutions of fourth-order differential equations. Moreover, we establish some new criterion for oscillation by using an integral averages condition of Philos-type, also Hille and Nehari-type. Some examples are provided to illustrate the main results. |
| first_indexed | 2024-12-10T06:50:18Z |
| format | Article |
| id | doaj.art-ae0466763fd84f4f88b854054a92619b |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-12-10T06:50:18Z |
| publishDate | 2020-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-ae0466763fd84f4f88b854054a92619b2022-12-22T01:58:34ZengMDPI AGSymmetry2073-89942020-01-0112113610.3390/sym12010136sym12010136New Results for Oscillatory Behavior of Fourth-Order Differential EquationsRami Ahmad El-Nabulsi0Osama Moaaz1Omar Bazighifan2Athens Institute for Education and Research, Mathematics and Physics Divisions, 10671 Athens, GreeceDepartment of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, EgyptDepartment of Mathematics, Faculty of Science, Hadhramout University, Hadhramout 50512, YemenOur aim in the present paper is to employ the Riccatti transformation which differs from those reported in some literature and comparison principles with the second-order differential equations, to establish some new conditions for the oscillation of all solutions of fourth-order differential equations. Moreover, we establish some new criterion for oscillation by using an integral averages condition of Philos-type, also Hille and Nehari-type. Some examples are provided to illustrate the main results.https://www.mdpi.com/2073-8994/12/1/136oscillatory solutionsnonoscillatory solutionsfourth-orderdelay differential equationsriccati transformationcomparison theorem |
| spellingShingle | Rami Ahmad El-Nabulsi Osama Moaaz Omar Bazighifan New Results for Oscillatory Behavior of Fourth-Order Differential Equations Symmetry oscillatory solutions nonoscillatory solutions fourth-order delay differential equations riccati transformation comparison theorem |
| title | New Results for Oscillatory Behavior of Fourth-Order Differential Equations |
| title_full | New Results for Oscillatory Behavior of Fourth-Order Differential Equations |
| title_fullStr | New Results for Oscillatory Behavior of Fourth-Order Differential Equations |
| title_full_unstemmed | New Results for Oscillatory Behavior of Fourth-Order Differential Equations |
| title_short | New Results for Oscillatory Behavior of Fourth-Order Differential Equations |
| title_sort | new results for oscillatory behavior of fourth order differential equations |
| topic | oscillatory solutions nonoscillatory solutions fourth-order delay differential equations riccati transformation comparison theorem |
| url | https://www.mdpi.com/2073-8994/12/1/136 |
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