Nonexitence of nontrivial solutions to Dirichlet problems for the fractional Laplacian
Texas State University, Department of Mathematics
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.
Fractional Laplacian, Dirichlet problem, Nonexistence of solutions
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.