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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.04117 |
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| _version_ | 1866912183988781056 |
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| author | Feulefack, Pierre Aime Zongo, Emmanuel Wend-Benedo |
| author_facet | Feulefack, Pierre Aime Zongo, Emmanuel Wend-Benedo |
| contents | In this paper, we investigate on a bounded open set of $\mathbb{R}^N$ with smooth boundary, an eigenvalue problem involving the sum of nonlocal operators $(-Δ)_p^{s_1}+ (-Δ)_q^{s_2}$ with $s_1,s_2\in (0,1)$, $p,q\in (1,\infty)$ and subject to the corresponding homogeneous nonlocal $(p,q)$-Neumann boundary condition. A careful analysis of the considered problem leads us to a complete description of the set of eigenvalues as being the precise interval $\{0\}\cup(λ_{1}(s_2,q),\infty)$, where $λ_{1}(s_2,q)$ is the first nonzero eigenvalue of the homogeneous fractional $q$-Laplacian under nonlocal $q$-Neumann boundary condition. Furthermore, we establish that every eigenfunctions is globally bounded. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_04117 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Eigenvalues of nonlinear $(p,q)$-fractional Laplace operators under nonlocal Neumann conditions Feulefack, Pierre Aime Zongo, Emmanuel Wend-Benedo Analysis of PDEs 35A09, 35B50, 35B65, 35R11, 35J67, 47A75 In this paper, we investigate on a bounded open set of $\mathbb{R}^N$ with smooth boundary, an eigenvalue problem involving the sum of nonlocal operators $(-Δ)_p^{s_1}+ (-Δ)_q^{s_2}$ with $s_1,s_2\in (0,1)$, $p,q\in (1,\infty)$ and subject to the corresponding homogeneous nonlocal $(p,q)$-Neumann boundary condition. A careful analysis of the considered problem leads us to a complete description of the set of eigenvalues as being the precise interval $\{0\}\cup(λ_{1}(s_2,q),\infty)$, where $λ_{1}(s_2,q)$ is the first nonzero eigenvalue of the homogeneous fractional $q$-Laplacian under nonlocal $q$-Neumann boundary condition. Furthermore, we establish that every eigenfunctions is globally bounded. |
| title | Eigenvalues of nonlinear $(p,q)$-fractional Laplace operators under nonlocal Neumann conditions |
| topic | Analysis of PDEs 35A09, 35B50, 35B65, 35R11, 35J67, 47A75 |
| url | https://arxiv.org/abs/2501.04117 |