Some nonlinear problems for the superposition of fractional operators with Neumann boundary conditions
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866910048723140608 |
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| author | Dipierro, Serena Lippi, Edoardo Proietti Sportelli, Caterina Valdinoci, Enrico |
| author_facet | Dipierro, Serena Lippi, Edoardo Proietti Sportelli, Caterina Valdinoci, Enrico |
| contents | We discuss the existence theory of a nonlinear problem of nonlocal type subject to Neumann boundary conditions. Differently from the existing literature, the elliptic operator under consideration is obtained as a superposition of operators of mixed order.
The setting that we introduce is very general and comprises, for instance, the sum of two fractional Laplacians, or of a fractional Laplacian and a Laplacian, as particular cases (the situation in which there are infinitely many operators, and even a continuous distribution of operators, can be considered as well).
New bits of functional analysis are introduced to deal with this problem. An eigenvalue analysis divides the existence theory into two streams, one related to a Mountain Pass method, the other to a Linking technique. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_11091 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Some nonlinear problems for the superposition of fractional operators with Neumann boundary conditions Dipierro, Serena Lippi, Edoardo Proietti Sportelli, Caterina Valdinoci, Enrico Analysis of PDEs We discuss the existence theory of a nonlinear problem of nonlocal type subject to Neumann boundary conditions. Differently from the existing literature, the elliptic operator under consideration is obtained as a superposition of operators of mixed order. The setting that we introduce is very general and comprises, for instance, the sum of two fractional Laplacians, or of a fractional Laplacian and a Laplacian, as particular cases (the situation in which there are infinitely many operators, and even a continuous distribution of operators, can be considered as well). New bits of functional analysis are introduced to deal with this problem. An eigenvalue analysis divides the existence theory into two streams, one related to a Mountain Pass method, the other to a Linking technique. |
| title | Some nonlinear problems for the superposition of fractional operators with Neumann boundary conditions |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2404.11091 |