Existence and multiplicity of $a$-harmonic solutions for a Steklov problem with variable exponents
Using variational methods, we prove in a different cases the existence and multiplicity of $a$-harmonic solutions for the following elleptic problem:\begin{equation*}\begin{gathered}div(a(x, \nabla u))=0, \quad \text{in }\Omega, \\a(x, \nabla u).\nu=f(x,u), \quad \text{on } \partial\Omega,\end{gathe...
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| Format: | Article |
| Language: | English |
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Sociedade Brasileira de Matemática
2018-04-01
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| Series: | Boletim da Sociedade Paranaense de Matemática |
| Subjects: | |
| Online Access: | https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/31071 |
| _version_ | 1797633393044750336 |
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| author | Abdellah Ahmed Zerouali Belhadj Karim Omar Chakrone |
| author_facet | Abdellah Ahmed Zerouali Belhadj Karim Omar Chakrone |
| author_sort | Abdellah Ahmed Zerouali |
| collection | DOAJ |
| description | Using variational methods, we prove in a different cases the existence and multiplicity of $a$-harmonic solutions for the following elleptic problem:\begin{equation*}\begin{gathered}div(a(x, \nabla u))=0, \quad \text{in }\Omega, \\a(x, \nabla u).\nu=f(x,u), \quad \text{on } \partial\Omega,\end{gathered}\end{equation*} where $\Omega\subset\mathbb{R}^N(N \geq 2)$ is a bounded domain ofsmooth boundary $\partial\Omega$ and $\nu$ is the outward normalvector on $\partial\Omega$. $f: \partial\Omega\times \mathbb{R} \rightarrow \mathbb{R},$ $a: \overline{\Omega}\times \mathbb{R}^{N} \rightarrow\mathbb{R}^{N},$ are fulfilling appropriate conditions. |
| first_indexed | 2024-03-11T11:53:27Z |
| format | Article |
| id | doaj.art-0d27568b1adc410399f0e5a07d971c54 |
| institution | Directory Open Access Journal |
| issn | 0037-8712 2175-1188 |
| language | English |
| last_indexed | 2024-03-11T11:53:27Z |
| publishDate | 2018-04-01 |
| publisher | Sociedade Brasileira de Matemática |
| record_format | Article |
| series | Boletim da Sociedade Paranaense de Matemática |
| spelling | doaj.art-0d27568b1adc410399f0e5a07d971c542023-11-08T20:10:25ZengSociedade Brasileira de MatemáticaBoletim da Sociedade Paranaense de Matemática0037-87122175-11882018-04-0136210.5269/bspm.v36i2.3107115440Existence and multiplicity of $a$-harmonic solutions for a Steklov problem with variable exponentsAbdellah Ahmed Zerouali0Belhadj Karim1Omar Chakrone2Centre Régional des Métiers de l’Éducation et de la Formation, FèsFaculté des Sciences et TéchniquesFaculté des Sciences OujdaUsing variational methods, we prove in a different cases the existence and multiplicity of $a$-harmonic solutions for the following elleptic problem:\begin{equation*}\begin{gathered}div(a(x, \nabla u))=0, \quad \text{in }\Omega, \\a(x, \nabla u).\nu=f(x,u), \quad \text{on } \partial\Omega,\end{gathered}\end{equation*} where $\Omega\subset\mathbb{R}^N(N \geq 2)$ is a bounded domain ofsmooth boundary $\partial\Omega$ and $\nu$ is the outward normalvector on $\partial\Omega$. $f: \partial\Omega\times \mathbb{R} \rightarrow \mathbb{R},$ $a: \overline{\Omega}\times \mathbb{R}^{N} \rightarrow\mathbb{R}^{N},$ are fulfilling appropriate conditions. https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/31071Variable exponentsElliptic problemNonlinear boundary condition$a$-harmonic solutionsRecceri's variational principlemountain pass theorem |
| spellingShingle | Abdellah Ahmed Zerouali Belhadj Karim Omar Chakrone Existence and multiplicity of $a$-harmonic solutions for a Steklov problem with variable exponents Boletim da Sociedade Paranaense de Matemática Variable exponents Elliptic problem Nonlinear boundary condition $a$-harmonic solutions Recceri's variational principle mountain pass theorem |
| title | Existence and multiplicity of $a$-harmonic solutions for a Steklov problem with variable exponents |
| title_full | Existence and multiplicity of $a$-harmonic solutions for a Steklov problem with variable exponents |
| title_fullStr | Existence and multiplicity of $a$-harmonic solutions for a Steklov problem with variable exponents |
| title_full_unstemmed | Existence and multiplicity of $a$-harmonic solutions for a Steklov problem with variable exponents |
| title_short | Existence and multiplicity of $a$-harmonic solutions for a Steklov problem with variable exponents |
| title_sort | existence and multiplicity of a harmonic solutions for a steklov problem with variable exponents |
| topic | Variable exponents Elliptic problem Nonlinear boundary condition $a$-harmonic solutions Recceri's variational principle mountain pass theorem |
| url | https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/31071 |
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