Properties of fractional p-Laplace equations with sign-changing potential
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909167370895360 |
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| author | Duan, Yubo Wei, Yawei |
| author_facet | Duan, Yubo Wei, Yawei |
| contents | In this paper, we consider the nonlinear equation involving the fractional p-Laplacian with sign-changing potential. This model draws inspiration from De Giorgi Conjecture. There are two main results in this paper. Firstly, we obtain that the solution is radially symmetric within the bounded domain, by applying the moving plane method. Secondly, by exploiting the idea of the sliding method, we construct the appropriate auxiliary functions to prove that the solution is monotone increasing in some direction in the unbounded domain. The different properties of the solution in bounded and unbounded domains are mainly attributed to the inherent non-locality of the fractional p-Laplacian. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_08196 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Properties of fractional p-Laplace equations with sign-changing potential Duan, Yubo Wei, Yawei Analysis of PDEs 35R11, 35J60, 35B40 In this paper, we consider the nonlinear equation involving the fractional p-Laplacian with sign-changing potential. This model draws inspiration from De Giorgi Conjecture. There are two main results in this paper. Firstly, we obtain that the solution is radially symmetric within the bounded domain, by applying the moving plane method. Secondly, by exploiting the idea of the sliding method, we construct the appropriate auxiliary functions to prove that the solution is monotone increasing in some direction in the unbounded domain. The different properties of the solution in bounded and unbounded domains are mainly attributed to the inherent non-locality of the fractional p-Laplacian. |
| title | Properties of fractional p-Laplace equations with sign-changing potential |
| topic | Analysis of PDEs 35R11, 35J60, 35B40 |
| url | https://arxiv.org/abs/2404.08196 |