Fuchsian-type singularity for the Finsler $p$-Laplacian with potential

Let $\mathrm{\Omega }\subseteq {\mathbb{R}}^n$ ($2\le n\in \mathbb{N}$) be a domain and let $\zeta \in \{0,\mathrm{\infty }\}$ be an isolated point of the boundary of $\mathrm{\Omega }$ in the one-point compactification of ${\mathbb{R}}^n$ with the ideal point $\mathrm{\infty }$. Under some further conditions, we study Fuchsian-type singularity at $\zeta$ for the Finsler $p$-Laplace equation with a potential $$-\mathrm{d}\mathrm{i}\mathrm{v}\mathcal{A}(x,\mathrm{\nabla }u)+V\mathrm{\mid }u{\mathrm{\mid }}^{p-2}u=0(1<p<\mathrm{\infty })in\mathrm{\Omega },$$ where $\mathcal{A}(x,\xi )\triangleq {\mathrm{\nabla }}_{\xi }(H(x,\xi {)}^p\mathrm{/}p)$ for almost all $x\in \mathrm{\Omega }$ and all $\xi \in {\mathbb{R}}^n$, $H$ is a family of norms on ${\mathbb{R}}^n$ ($n\ge 2$) parameterized by points $x\in \mathrm{\Omega }$, and $V$ belongs to a local Morrey space. In particular, we investigate asymptotic behaviors of positive solutions of the equation near $\zeta$ and asymptotic behaviors of their quotients.