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

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 (\mathcal{P})\begin{cases}-\Delta^{H}_{p} u=\theta\frac{u^{p-1}}{H^0(x)^p}+\frac{1}{u^\gamma}+f(x,u)&\text{in } \Omega,\\\ u>0&\text{in } \Omega,\\\ u=0&\text{in } \partial\Omega,\end{cases} 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} .