Fractional Dirichlet problems with singular and non-locally convective reaction
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915025901322240 |
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| author | Gambera, Laura Marano, Salvatore A. |
| author_facet | Gambera, Laura Marano, Salvatore A. |
| contents | In this paper, the existence of positive weak solutions to a Dirichlet problem driven by the fractional $(p,q)$-Laplacian and with reaction both weakly singular and non-locally convective (i.e., depending on the distributional Riesz gradient of solutions) is established. Due to the nature of the right-hand side, we address the problem via sub-super solution methods, combined with variational techniques, truncation arguments, as well as fixed point results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_11026 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fractional Dirichlet problems with singular and non-locally convective reaction Gambera, Laura Marano, Salvatore A. Analysis of PDEs 35J60, 35J75, 35D30 In this paper, the existence of positive weak solutions to a Dirichlet problem driven by the fractional $(p,q)$-Laplacian and with reaction both weakly singular and non-locally convective (i.e., depending on the distributional Riesz gradient of solutions) is established. Due to the nature of the right-hand side, we address the problem via sub-super solution methods, combined with variational techniques, truncation arguments, as well as fixed point results. |
| title | Fractional Dirichlet problems with singular and non-locally convective reaction |
| topic | Analysis of PDEs 35J60, 35J75, 35D30 |
| url | https://arxiv.org/abs/2411.11026 |