Nonlocal Dirichlet problems involving the Logarithmic $p$-Laplacian
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917170458394624 |
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| author | Arora, Rakesh Hajaiej, Hichem Perera, Kanishka |
| author_facet | Arora, Rakesh Hajaiej, Hichem Perera, Kanishka |
| contents | In this work, we show the existence of an unbounded sequence of minimax eigenvalues for the logarithmic $p$-Laplacian via the $\mathbb{Z}_2$-cohomological index of Fadell and Rabinowitz. As an application of these minimax eigenvalues and $p$-logarithmic Sobolev inequality proved in [4], we prove new existence results for nonlocal Dirichlet problems involving logarithmic $p$-Laplacian and nonlinearities with $p$-superlinear and subcritical growth at infinity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_21959 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonlocal Dirichlet problems involving the Logarithmic $p$-Laplacian Arora, Rakesh Hajaiej, Hichem Perera, Kanishka Analysis of PDEs In this work, we show the existence of an unbounded sequence of minimax eigenvalues for the logarithmic $p$-Laplacian via the $\mathbb{Z}_2$-cohomological index of Fadell and Rabinowitz. As an application of these minimax eigenvalues and $p$-logarithmic Sobolev inequality proved in [4], we prove new existence results for nonlocal Dirichlet problems involving logarithmic $p$-Laplacian and nonlinearities with $p$-superlinear and subcritical growth at infinity. |
| title | Nonlocal Dirichlet problems involving the Logarithmic $p$-Laplacian |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2512.21959 |