Eigenvalues of the $p(x)-$biharmonic operator with indefinite weight] {Eigenvalues of the $p(x)-$biharmonic operator with indefinite weight under Neumann boundary conditions
In this paper we will study the existence of solutions for the nonhomogeneous elliptic equation with variable exponent $\Delta^2_{p(x)} u=\lambda V(x) |u|^{q(x)-2} u$, in a smooth bounded domain,under Neumann boundary conditions, where $\lambda$ is a positive real number, $p,q: \overline{\Omega} \ri...
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| Format: | Article |
| Language: | English |
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Sociedade Brasileira de Matemática
2018-01-01
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| Series: | Boletim da Sociedade Paranaense de Matemática |
| Subjects: | |
| Online Access: | http://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/31363 |
| _version_ | 1818022262664593408 |
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| author | Zakaria El Allali Said Taarabti Khalil Ben Haddouch |
| author_facet | Zakaria El Allali Said Taarabti Khalil Ben Haddouch |
| author_sort | Zakaria El Allali |
| collection | DOAJ |
| description | In this paper we will study the existence of solutions for the nonhomogeneous elliptic equation with variable exponent $\Delta^2_{p(x)} u=\lambda V(x) |u|^{q(x)-2} u$, in a smooth bounded domain,under Neumann boundary conditions, where $\lambda$ is a positive real number, $p,q: \overline{\Omega} \rightarrow \mathbb{R}$, are continuous functions, and $V$ is an indefinite weight function. Considering different situations concerning the growth rates involved in the above quoted problem, we will prove the existence of a continuous family of eigenvalues. |
| first_indexed | 2024-04-14T08:29:54Z |
| format | Article |
| id | doaj.art-685516d219a044feb688b5a44b927579 |
| institution | Directory Open Access Journal |
| issn | 0037-8712 2175-1188 |
| language | English |
| last_indexed | 2024-04-14T08:29:54Z |
| publishDate | 2018-01-01 |
| publisher | Sociedade Brasileira de Matemática |
| record_format | Article |
| series | Boletim da Sociedade Paranaense de Matemática |
| spelling | doaj.art-685516d219a044feb688b5a44b9275792022-12-22T02:03:57ZengSociedade Brasileira de MatemáticaBoletim da Sociedade Paranaense de Matemática0037-87122175-11882018-01-0136119521310.5269/bspm.v36i1.3136315359Eigenvalues of the $p(x)-$biharmonic operator with indefinite weight] {Eigenvalues of the $p(x)-$biharmonic operator with indefinite weight under Neumann boundary conditionsZakaria El Allali0Said Taarabti1Khalil Ben Haddouch2Department of Mathematics, and Computer Polydisciplinary Faculty of Nador, The university Mohammed Premier, Oujda, MoroccoDepartment of Mathematics and Computer Polydisciplinary Faculty of Nador, The university Mohammed Premier, Oujda, MoroccoDepartment of Mathematics and Computer Science, Faculty of Science, University Mohammed Premier, Oujda, MoroccoIn this paper we will study the existence of solutions for the nonhomogeneous elliptic equation with variable exponent $\Delta^2_{p(x)} u=\lambda V(x) |u|^{q(x)-2} u$, in a smooth bounded domain,under Neumann boundary conditions, where $\lambda$ is a positive real number, $p,q: \overline{\Omega} \rightarrow \mathbb{R}$, are continuous functions, and $V$ is an indefinite weight function. Considering different situations concerning the growth rates involved in the above quoted problem, we will prove the existence of a continuous family of eigenvalues.http://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/31363Fourth order elliptic equationvariable exponentNeumann boundary conditionsEkeland variational principle |
| spellingShingle | Zakaria El Allali Said Taarabti Khalil Ben Haddouch Eigenvalues of the $p(x)-$biharmonic operator with indefinite weight] {Eigenvalues of the $p(x)-$biharmonic operator with indefinite weight under Neumann boundary conditions Boletim da Sociedade Paranaense de Matemática Fourth order elliptic equation variable exponent Neumann boundary conditions Ekeland variational principle |
| title | Eigenvalues of the $p(x)-$biharmonic operator with indefinite weight] {Eigenvalues of the $p(x)-$biharmonic operator with indefinite weight under Neumann boundary conditions |
| title_full | Eigenvalues of the $p(x)-$biharmonic operator with indefinite weight] {Eigenvalues of the $p(x)-$biharmonic operator with indefinite weight under Neumann boundary conditions |
| title_fullStr | Eigenvalues of the $p(x)-$biharmonic operator with indefinite weight] {Eigenvalues of the $p(x)-$biharmonic operator with indefinite weight under Neumann boundary conditions |
| title_full_unstemmed | Eigenvalues of the $p(x)-$biharmonic operator with indefinite weight] {Eigenvalues of the $p(x)-$biharmonic operator with indefinite weight under Neumann boundary conditions |
| title_short | Eigenvalues of the $p(x)-$biharmonic operator with indefinite weight] {Eigenvalues of the $p(x)-$biharmonic operator with indefinite weight under Neumann boundary conditions |
| title_sort | eigenvalues of the p x biharmonic operator with indefinite weight eigenvalues of the p x biharmonic operator with indefinite weight under neumann boundary conditions |
| topic | Fourth order elliptic equation variable exponent Neumann boundary conditions Ekeland variational principle |
| url | http://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/31363 |
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