Infinitely many solutions for an anisotropic differential inclusion on unbounded domains
The problem deals with the anisotropic $p(x)$-Laplacian operator where $p_i$ are Lipschitz continuous functions $2\leq p_i(x)<N$ for all $x\in \mathbb{R}^N$ and $i\in\{1,\dots,N\}$. Assume $p^o_N(x)=\max_{1\leq i\leq N} p_i(x)$, $a\in L^1_+(\mathbb{R}^N)\cap L^{\frac{N}{p^o_N(x)-1}}(\mathbb{R}^N)...
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| Format: | Article |
| Language: | English |
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University of Szeged
2024-07-01
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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=11060 |
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| _version_ | 1841533473765982208 |
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| author | Giovany Figueiredo Abdolrahman Razani |
| author_facet | Giovany Figueiredo Abdolrahman Razani |
| author_sort | Giovany Figueiredo |
| collection | DOAJ |
| description | The problem deals with the anisotropic $p(x)$-Laplacian operator where $p_i$ are Lipschitz continuous functions $2\leq p_i(x)<N$ for all $x\in \mathbb{R}^N$ and $i\in\{1,\dots,N\}$. Assume $p^o_N(x)=\max_{1\leq i\leq N} p_i(x)$, $a\in L^1_+(\mathbb{R}^N)\cap L^{\frac{N}{p^o_N(x)-1}}(\mathbb{R}^N)$, $F(x,t)$ is locally Lipschitz in the $t$-variable integrand and $\partial F(x,t)$ is the subdifferential with respect to the $t$-variable in the sense of Clarke. By establishing the existence of infinitely many solutions, we achieve a first result within the anisotropic framework. |
| format | Article |
| id | doaj-art-2f4d3439b0d641de827aeb89c0e7eb98 |
| institution | Kabale University |
| issn | 1417-3875 |
| language | English |
| publishDate | 2024-07-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj-art-2f4d3439b0d641de827aeb89c0e7eb982025-01-15T21:24:58ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752024-07-0120243311710.14232/ejqtde.2024.1.3311060Infinitely many solutions for an anisotropic differential inclusion on unbounded domainsGiovany Figueiredo0https://orcid.org/0000-0003-1697-1592Abdolrahman Razanihttps://orcid.org/0000-0002-3092-3530Universidade de Brasília, Brasília, BrazilThe problem deals with the anisotropic $p(x)$-Laplacian operator where $p_i$ are Lipschitz continuous functions $2\leq p_i(x)<N$ for all $x\in \mathbb{R}^N$ and $i\in\{1,\dots,N\}$. Assume $p^o_N(x)=\max_{1\leq i\leq N} p_i(x)$, $a\in L^1_+(\mathbb{R}^N)\cap L^{\frac{N}{p^o_N(x)-1}}(\mathbb{R}^N)$, $F(x,t)$ is locally Lipschitz in the $t$-variable integrand and $\partial F(x,t)$ is the subdifferential with respect to the $t$-variable in the sense of Clarke. By establishing the existence of infinitely many solutions, we achieve a first result within the anisotropic framework.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=11060anisotropic $p(x)$-laplaciandifferential inclusion problemlocally lipschitz functioninfinitely many solutionsvariational method |
| spellingShingle | Giovany Figueiredo Abdolrahman Razani Infinitely many solutions for an anisotropic differential inclusion on unbounded domains Electronic Journal of Qualitative Theory of Differential Equations anisotropic $p(x)$-laplacian differential inclusion problem locally lipschitz function infinitely many solutions variational method |
| title | Infinitely many solutions for an anisotropic differential inclusion on unbounded domains |
| title_full | Infinitely many solutions for an anisotropic differential inclusion on unbounded domains |
| title_fullStr | Infinitely many solutions for an anisotropic differential inclusion on unbounded domains |
| title_full_unstemmed | Infinitely many solutions for an anisotropic differential inclusion on unbounded domains |
| title_short | Infinitely many solutions for an anisotropic differential inclusion on unbounded domains |
| title_sort | infinitely many solutions for an anisotropic differential inclusion on unbounded domains |
| topic | anisotropic $p(x)$-laplacian differential inclusion problem locally lipschitz function infinitely many solutions variational method |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=11060 |
| work_keys_str_mv | AT giovanyfigueiredo infinitelymanysolutionsforananisotropicdifferentialinclusiononunboundeddomains AT abdolrahmanrazani infinitelymanysolutionsforananisotropicdifferentialinclusiononunboundeddomains |