Choquard equations with critical exponential nonlinearities in the zero mass case
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912496892248064 |
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| author | Romani, Giulio |
| author_facet | Romani, Giulio |
| contents | We investigate Choquard equations in $\mathbb R^N$ driven by a weighted $N$-Laplace operator and with polynomial kernel and zero mass. Since the setting is limiting for the Sobolev embedding, we work with nonlinearities which may grow up to the critical exponential. We establish existence of a positive solution by variational methods, completing the analysis in [Romani, ArXiv preprint 2023], where the case of a logarithmic kernel was considered. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_15965 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Choquard equations with critical exponential nonlinearities in the zero mass case Romani, Giulio Analysis of PDEs 35A15, 35J20, 35J60, 35B33 We investigate Choquard equations in $\mathbb R^N$ driven by a weighted $N$-Laplace operator and with polynomial kernel and zero mass. Since the setting is limiting for the Sobolev embedding, we work with nonlinearities which may grow up to the critical exponential. We establish existence of a positive solution by variational methods, completing the analysis in [Romani, ArXiv preprint 2023], where the case of a logarithmic kernel was considered. |
| title | Choquard equations with critical exponential nonlinearities in the zero mass case |
| topic | Analysis of PDEs 35A15, 35J20, 35J60, 35B33 |
| url | https://arxiv.org/abs/2404.15965 |