Jose Carmona, Alexis Molino
Abstract:
In this article we prove that there are no nontrivial solutions to
the Dirichlet problem for the fractional Laplacian
$$ \displaylines{(-\Delta)^s u =f(u) \quad \text{in }\Omega,\\ u=0 \quad \text{in } \mathbb{R}^N \backslash \Omega,}$$ where
\(\Omega \subset \mathbb{R}^N\) (\(N\geq 1\)) is a bounded domain,
and f is locally Lipschitz with non-positive primitive \(F(t)= \int_0^t f(\tau)d\tau\).
Submitted March 30, 2022 Published February 17, 2023.
Math Subject Classifications: 35J05, 35J15, 35J25.
Key Words: Fractional Laplacian; Dirichlet problem; nonexistence of solutions.
DOI: https://doi.org/10.58997/ejde.2023.16
Show me the PDF file (337 KB), TEX file for this article.
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José Carmona Departamento de Matemáticas Universidad de Almería Facultad de Ciencias Experimentales Ctra. de Sacramento sn. 04120 La Cañada de San Urbano. Almería, Spain email: jcarmona@ual.es |
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Alexis Molino Departamento de Matemáticas Universidad de Almería Facultad de Ciencias Experimentales Ctra. de Sacramento sn. 04120 La Cañada de San Urbano. Almería, Spain email: amolino@ual.es |
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