Liouville-type results for semilinear inequalities involving the Dunkl Laplacian operator

Let Δk be the Dunkl generalized Laplacian operator associated to a root system R of RN and a nonnegative multiplicity function k defined on R and invariant by the finite reflection group W. In this paper, we establish Liouville-type theorems for the semilinear inequality −Δku≥|u|p in RN and the system of inequalities −Δku≥|v|p, −Δkv≥|u|q in RN, where N≥1 and p,q>1. To the best of our knowledge, this contribution is the first work dealing with Liouville-type results for nonlinear problems involving the Dunkl Laplacian.