Three non-zero solutions of a Neumann eigenvalue problems involving the fractional p-Laplacian
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913732793204736 |
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| author | Gandal, Somnath |
| author_facet | Gandal, Somnath |
| contents | In the present paper, we establish a multiplicity result for a following class of nonlocal Neumann eigenvalue problems involving the fractional p-Laplacian.
\begin{align} \begin{cases}
(-Δ)^{s}_{p}u + a(x) \abs{u}^{p-2}u =λh(x,u) & \text {in } Ω,
\mathcal{N}_{s,p}u=0 & \text {in } \mathbb{R}^N \setminus \overlineΩ,
\end{cases}
\end{align}
Precisely, we demonstrate the existence of an open interval for positive eigenvalues $λ$, for which the problem has at least three non-zero solutions in $W^{s,p}_Ω.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_09323 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Three non-zero solutions of a Neumann eigenvalue problems involving the fractional p-Laplacian Gandal, Somnath Analysis of PDEs 35R11, 35D30, 35A15, 35J60, 35S15, 47G20 In the present paper, we establish a multiplicity result for a following class of nonlocal Neumann eigenvalue problems involving the fractional p-Laplacian. \begin{align} \begin{cases} (-Δ)^{s}_{p}u + a(x) \abs{u}^{p-2}u =λh(x,u) & \text {in } Ω, \mathcal{N}_{s,p}u=0 & \text {in } \mathbb{R}^N \setminus \overlineΩ, \end{cases} \end{align} Precisely, we demonstrate the existence of an open interval for positive eigenvalues $λ$, for which the problem has at least three non-zero solutions in $W^{s,p}_Ω.$ |
| title | Three non-zero solutions of a Neumann eigenvalue problems involving the fractional p-Laplacian |
| topic | Analysis of PDEs 35R11, 35D30, 35A15, 35J60, 35S15, 47G20 |
| url | https://arxiv.org/abs/2503.09323 |