For a suitable function $A:\mathbb{ R}^n\to \mathbb{ R}^n$, we introduce the $A$-Laplacian in the Dunkl framework as $\Delta_{ k,A}(u) =\text{ div}_k(A(\nabla_ku))$, where $\nabla_k$ is the Dunkl-gradient operator associated with the multiplicity function $k$ and the root system $\mathcal{ R}$. We derive the local and global Caccioppoli-type inequality for an element $u$ in the Dunkl-Orlicz-Sobolev space, satisfying the Dunkl-differential inequality $$ -\Delta_{ k, A}(u) \geq b\Phi(u)\chi_{ \{ u>0\}}. $$ Using the Caccioppoli inequality, we establish a sufficient condition for the nonexistence of a nonzero solution $u$ to the Dunkl-differential inequality.
Categories: math.AP math.FA