Nonlinear differential equations of fourth-order: Qualitative properties of the solutions
In this paper, we study the oscillation of solutions for a fourth-order neutral nonlinear differential equation, driven by a $p$-Laplace differential operator of the form \begin{equation*} \begin{cases} \left( r\left( t\right) \Phi _{p_{1}}[w^{\prime \prime \prime }\left( t\right) ]\right) ^{\prime...
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| Format: | Article |
| Language: | English |
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AIMS Press
2020-08-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/10.3934/math.2020414/fulltext.html |
| _version_ | 1828526405679316992 |
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| author | Omar Bazighifan |
| author_facet | Omar Bazighifan |
| author_sort | Omar Bazighifan |
| collection | DOAJ |
| description | In this paper, we study the oscillation of solutions for a fourth-order neutral nonlinear differential equation, driven by a $p$-Laplace differential operator of the form \begin{equation*} \begin{cases} \left( r\left( t\right) \Phi _{p_{1}}[w^{\prime \prime \prime }\left( t\right) ]\right) ^{\prime }+q\left( t\right) \Phi _{p_{2}}\left( u\left( \vartheta \left( t\right) \right) \right) =0, & \\ r\left( t\right) >0,\ r^{\prime }\left( t\right) \geq 0,\ t\geq t_{0}>0, & \end{cases} \end{equation*} The oscillation criteria for these equations have been obtained. Furthermore, some examples are given to illustrate the criteria. |
| first_indexed | 2024-12-11T21:23:06Z |
| format | Article |
| id | doaj.art-ea052dc249e249869ac9e85c080b42d7 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-11T21:23:06Z |
| publishDate | 2020-08-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-ea052dc249e249869ac9e85c080b42d72022-12-22T00:50:24ZengAIMS PressAIMS Mathematics2473-69882020-08-01566436644710.3934/math.2020414Nonlinear differential equations of fourth-order: Qualitative properties of the solutionsOmar Bazighifan01 Department of Mathematics, Faculty of Science, Hadhramout University, Hadhramout 50512, Yemen 2 Department of Mathematics, Faculty of Education, Seiyun University, Seiyun, YemenIn this paper, we study the oscillation of solutions for a fourth-order neutral nonlinear differential equation, driven by a $p$-Laplace differential operator of the form \begin{equation*} \begin{cases} \left( r\left( t\right) \Phi _{p_{1}}[w^{\prime \prime \prime }\left( t\right) ]\right) ^{\prime }+q\left( t\right) \Phi _{p_{2}}\left( u\left( \vartheta \left( t\right) \right) \right) =0, & \\ r\left( t\right) >0,\ r^{\prime }\left( t\right) \geq 0,\ t\geq t_{0}>0, & \end{cases} \end{equation*} The oscillation criteria for these equations have been obtained. Furthermore, some examples are given to illustrate the criteria.https://www.aimspress.com/article/10.3934/math.2020414/fulltext.htmlfourth-order differential equationsneutral delayoscillation |
| spellingShingle | Omar Bazighifan Nonlinear differential equations of fourth-order: Qualitative properties of the solutions AIMS Mathematics fourth-order differential equations neutral delay oscillation |
| title | Nonlinear differential equations of fourth-order: Qualitative properties of the solutions |
| title_full | Nonlinear differential equations of fourth-order: Qualitative properties of the solutions |
| title_fullStr | Nonlinear differential equations of fourth-order: Qualitative properties of the solutions |
| title_full_unstemmed | Nonlinear differential equations of fourth-order: Qualitative properties of the solutions |
| title_short | Nonlinear differential equations of fourth-order: Qualitative properties of the solutions |
| title_sort | nonlinear differential equations of fourth order qualitative properties of the solutions |
| topic | fourth-order differential equations neutral delay oscillation |
| url | https://www.aimspress.com/article/10.3934/math.2020414/fulltext.html |
| work_keys_str_mv | AT omarbazighifan nonlineardifferentialequationsoffourthorderqualitativepropertiesofthesolutions |