Existence of infinitely many solutions for a Steklov problem involving the p(x)-Laplace operator
In this article, we study the nonlinear Steklov boundary-value problem $$\begin{alignedat}{2} \Delta_{p(x)}u & =|u|^{p(x)-2}u \quad &&\text{in } \Omega, \\ |\nabla u|^{p(x)-2}\frac{\partial u}{\partial \nu} & = f(x,u) \quad &&\text{on } \partial\Omega. \end{alignedat}$$ We...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2014-05-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=2148 |
| _version_ | 1797830678559064064 |
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| author | Mostafa Allaoui Abdel Rachid El Amrouss Anass Ourraoui |
| author_facet | Mostafa Allaoui Abdel Rachid El Amrouss Anass Ourraoui |
| author_sort | Mostafa Allaoui |
| collection | DOAJ |
| description | In this article, we study the nonlinear Steklov boundary-value problem
$$\begin{alignedat}{2}
\Delta_{p(x)}u & =|u|^{p(x)-2}u \quad &&\text{in } \Omega, \\
|\nabla u|^{p(x)-2}\frac{\partial u}{\partial \nu} & = f(x,u) \quad
&&\text{on } \partial\Omega.
\end{alignedat}$$
We prove the existence of infinitely many non-negative solutions of the problem by applying a general variational principle due to B.\ Ricceri and the theory of the variable exponent Sobolev spaces. |
| first_indexed | 2024-04-09T13:39:55Z |
| format | Article |
| id | doaj.art-db8fb64b72004074a89a25f9f6fb6289 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:39:55Z |
| publishDate | 2014-05-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-db8fb64b72004074a89a25f9f6fb62892023-05-09T07:53:03ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752014-05-0120142011010.14232/ejqtde.2014.1.202148Existence of infinitely many solutions for a Steklov problem involving the p(x)-Laplace operatorMostafa Allaoui0Abdel Rachid El Amrouss1Anass Ourraoui2University Mohamed Ist, Oujda, MoroccoDepartment of Mathematics, Faculty of sciences, University Mohamed I, Oujda, MoroccoDepartment of Mathematics, Faculty of Sciences, University Mohamed I, Oujda, MoroccoIn this article, we study the nonlinear Steklov boundary-value problem $$\begin{alignedat}{2} \Delta_{p(x)}u & =|u|^{p(x)-2}u \quad &&\text{in } \Omega, \\ |\nabla u|^{p(x)-2}\frac{\partial u}{\partial \nu} & = f(x,u) \quad &&\text{on } \partial\Omega. \end{alignedat}$$ We prove the existence of infinitely many non-negative solutions of the problem by applying a general variational principle due to B.\ Ricceri and the theory of the variable exponent Sobolev spaces.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=2148$p(x)$-laplace operator; infinitely many solutions; variable exponent sobolev space; ricceri's variational principle |
| spellingShingle | Mostafa Allaoui Abdel Rachid El Amrouss Anass Ourraoui Existence of infinitely many solutions for a Steklov problem involving the p(x)-Laplace operator Electronic Journal of Qualitative Theory of Differential Equations $p(x)$-laplace operator; infinitely many solutions; variable exponent sobolev space; ricceri's variational principle |
| title | Existence of infinitely many solutions for a Steklov problem involving the p(x)-Laplace operator |
| title_full | Existence of infinitely many solutions for a Steklov problem involving the p(x)-Laplace operator |
| title_fullStr | Existence of infinitely many solutions for a Steklov problem involving the p(x)-Laplace operator |
| title_full_unstemmed | Existence of infinitely many solutions for a Steklov problem involving the p(x)-Laplace operator |
| title_short | Existence of infinitely many solutions for a Steklov problem involving the p(x)-Laplace operator |
| title_sort | existence of infinitely many solutions for a steklov problem involving the p x laplace operator |
| topic | $p(x)$-laplace operator; infinitely many solutions; variable exponent sobolev space; ricceri's variational principle |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=2148 |
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