Remarks on a comparison principle for a doubly singular quasilinear anisotropic problem

Abstract

In these notes, using some arguments of Montoro, Sciunzi, and Trombetta (2025), we prove a new general version of a comparison principle for sub-supersolutions to a singular quasilinear problem driven by the anisotropic operator. As a consequence, we deduce a uniqueness result for weak solutions to the problem

and then we analyze, in the anisotropic setting, the question of the existence of solutions to a subdiffusive problem in the whole ${\mathbb{R}}^N$.