Nonexitence of nontrivial solutions to Dirichlet problems for the fractional Laplacian
DOI:
https://doi.org/10.58997/ejde.2023.16Abstract
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 \(F(t)= \int_0^t f(\tau)d\tau\).
For more information see https://ejde.math.txstate.edu/Volumes/2023/16/abstr.html
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