id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-29	Carmona, José; Molino, Alexis	Nonexitence of nontrivial solutions to Dirichlet problems for the fractional Laplacian	2023	10	.pdf	application/pdf	4252	243	76	In this article we prove that there are no nontrivial solutions to the Dirichlet problem for the fractional Laplacian (−∆)su = f(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) Introduction In this work, we investigate the nonexistence of nontrivial bounded solutions for the Dirichlet problem for the fractional Laplacian (−∆)su = f(u) in Ω, u = 0 in RN \ Ω, (1.1) where Ω ⊂ RN (N ≥ 1) is a bounded domain with C1,1 regular boundary, ∂Ω, and f : R→ R is a locally Lipschitz sign-changing function.	cache/ejde-29.pdf	txt/ejde-29.txt