Semilinear equations associated with Dunkl Laplacian

2015/11/05 by Chrouda, Mohamed Ben, Mabrouk, Khalifa El, Hassine, Kods
#31B05 #31B15 #35J08 #35J61 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1511.02165

Abstract

Let Δ_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 Δ_ku=φ(u) in the unit ball of \mathbb R^d as well as in the whole space \mathbb R^d.

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