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WROCŁAW UNIVERSITY
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Contents of PMS, Vol. 38, Fasc. 1,
pages 249 - 269
DOI: 10.19195/0208-4147.38.2.1
 

BOUNDARY VALUE PROBLEMS FOR THE DUNKL LAPLACIAN

Mohamed Ben Chrouda
Khalifa El Mabrouk
Kods Hassine

Abstract: Let Δ k be the Dunkl Laplacian on ℝd associated with a reflection group W and a multiplicity function k . The purpose of this paper is to establish the existence and the uniqueness of a positive solution on the unit ball B of ℝd to the following boundary value problem:

Δ u = φ(u)in B and u = f on ∂B. k
We distinguish two cases of nonnegative perturbation φ : trivial and nontrivial.

2010 AMS Mathematics Subject Classification: Primary: 31B05, 60J45; Secondary: 35J08, 35J61.

Keywords and phrases: Dunkl Laplacian, Dirichlet problems, Green operators, semilinear equations.

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