Semilinear equations associated with Dunkl Laplacian

Abstract

Let ${\Delta }_k$ be the Dunkl Laplacian on ${\mathbb{R}}^d$ associated with a reflection group $W$ and a multiplicity function $k$. The purpose of this paper is to establish necessary and sufficient condition under which there exists a positive solution of the equation ${\Delta }_{k}u=\phi (u)$ in the unit ball of ${\mathbb{R}}^d$ as well as in the whole space ${\mathbb{R}}^d$.

23 pages

References in corpus (2)

• First Hitting Time of the Boundary of the Weyl Chamber by Radial Dunkl Processes
• Mean value property associated with the Dunkl Laplacian