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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2024-07-01
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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=11060 |
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| Summary: | 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. |
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| ISSN: | 1417-3875 |