A mixed local-nonlocal Hénon problem in $\mathbb{R}^N$
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914192845438976 |
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| author | Ochoa, Pablo Salort, Ariel |
| author_facet | Ochoa, Pablo Salort, Ariel |
| contents | In this article, we study a Hénon-type equation in $\mathbb{R}^N$ driven by a nonlinear operator given by the combination of a local and a nonlocal term. This equation was originally proposed to model spherically symmetric stellar clusters. Here, we prove that, under a suitable relation among the parameters, there exists a threshold separating the existence and non-existence of solutions. Moreover, we establish regularity properties of the solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_09794 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A mixed local-nonlocal Hénon problem in $\mathbb{R}^N$ Ochoa, Pablo Salort, Ariel Analysis of PDEs 35A15, 35A01, 35b06, 35R11, 35D30 In this article, we study a Hénon-type equation in $\mathbb{R}^N$ driven by a nonlinear operator given by the combination of a local and a nonlocal term. This equation was originally proposed to model spherically symmetric stellar clusters. Here, we prove that, under a suitable relation among the parameters, there exists a threshold separating the existence and non-existence of solutions. Moreover, we establish regularity properties of the solutions. |
| title | A mixed local-nonlocal Hénon problem in $\mathbb{R}^N$ |
| topic | Analysis of PDEs 35A15, 35A01, 35b06, 35R11, 35D30 |
| url | https://arxiv.org/abs/2512.09794 |