Nonexitence of nontrivial solutions to Dirichlet problems for the fractional Laplacian

Date
2023-02-17
Authors
Carmona, Jose
Molino, Alexis
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In this article we prove that there are no nontrivial solutions to the Dirichlet problem for the fractional Laplacian (-∆)su = ƒ(u) in Ω, u = 0 in ℝN\Ω, where Ω ⊂ ℝN (N≥1) is a bounded domain, and f is locally Lipschitz with non-positive primitive F(t) = ∫t0 ƒ(τ)dτ.
Description
Keywords
Fractional Laplacian, Dirichlet problem, Nonexistence of solutions
Citation
Carmona, J., & Molino, A. (2023). Nonexitence of nontrivial solutions to Dirichlet problems for the fractional Laplacian. <i>Electronic Journal of Differential Equations, 2023</i>(16), pp. 1-10.