On some differential equations involving a new kind of variable exponents
In this paper, we are concerned with some new first order differential equation defined on the whole real axis $\mathbb{R}.$ The principal part of the equation involves an operator with variable exponent $p$ depending on the variable $x \in \mathbb{R} $ through the unknown solution while the nonline...
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| Format: | Article |
| Language: | English |
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University of Szeged
2022-05-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
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| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=9605 |
| _version_ | 1797830466413264896 |
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| author | Sami Aouaoui |
| author_facet | Sami Aouaoui |
| author_sort | Sami Aouaoui |
| collection | DOAJ |
| description | In this paper, we are concerned with some new first order differential equation defined on the whole real axis $\mathbb{R}.$ The principal part of the equation involves an operator with variable exponent $p$ depending on the variable $x \in \mathbb{R} $ through the unknown solution while the nonlinear part involves the classical variable exponent $ p(x). $ Such kind of situation is very related to the presence of the variable exponent and has not been treated before. Our existence result of nontrivial solution cannot be reached using standard variational or topological methods of nonlinear analysis and some sophisticated arguments have to be employed. |
| first_indexed | 2024-04-09T13:36:32Z |
| format | Article |
| id | doaj.art-ce34069ba05d4ef499e7330f8437527f |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:36:32Z |
| publishDate | 2022-05-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-ce34069ba05d4ef499e7330f8437527f2023-05-09T07:53:11ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752022-05-0120222311810.14232/ejqtde.2022.1.239605On some differential equations involving a new kind of variable exponentsSami Aouaoui0ISMAI Kairouan, University of Kairouan, TunisiaIn this paper, we are concerned with some new first order differential equation defined on the whole real axis $\mathbb{R}.$ The principal part of the equation involves an operator with variable exponent $p$ depending on the variable $x \in \mathbb{R} $ through the unknown solution while the nonlinear part involves the classical variable exponent $ p(x). $ Such kind of situation is very related to the presence of the variable exponent and has not been treated before. Our existence result of nontrivial solution cannot be reached using standard variational or topological methods of nonlinear analysis and some sophisticated arguments have to be employed.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=9605$p(u)$-laplacianvariable exponentsschauder's fixed point theoremapproximation schemeweighted sobolev spaceexistence result |
| spellingShingle | Sami Aouaoui On some differential equations involving a new kind of variable exponents Electronic Journal of Qualitative Theory of Differential Equations $p(u)$-laplacian variable exponents schauder's fixed point theorem approximation scheme weighted sobolev space existence result |
| title | On some differential equations involving a new kind of variable exponents |
| title_full | On some differential equations involving a new kind of variable exponents |
| title_fullStr | On some differential equations involving a new kind of variable exponents |
| title_full_unstemmed | On some differential equations involving a new kind of variable exponents |
| title_short | On some differential equations involving a new kind of variable exponents |
| title_sort | on some differential equations involving a new kind of variable exponents |
| topic | $p(u)$-laplacian variable exponents schauder's fixed point theorem approximation scheme weighted sobolev space existence result |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=9605 |
| work_keys_str_mv | AT samiaouaoui onsomedifferentialequationsinvolvinganewkindofvariableexponents |