LAUSR

We study Liouville-type theorems and the asymptotic behaviour of positive solutions near an isolated singular point $$\zeta \in \partial \Omega \cup \{\infty \}$$ ζ ∈ ∂ Ω ∪ { ∞ } of the quasilinear elliptic equation $$\begin{aligned} -\text {div}(|\nabla u|_A^{p-2}A\nabla u)+V|u|^{p-2}u =0\quad \text {in } \Omega \setminus \{\zeta \}, \end{aligned}$$ - div ( | ∇ u | A p - 2 A ∇ u ) + V | u | p - 2 u = 0 in Ω \ { ζ } , where $$\Omega $$ Ω is a domain in $$\mathbb {R}^d$$ R d ( $$d\ge 2$$ d ≥ 2 ), and $$A=(a_{ij})\in L_\mathrm{loc}^{\infty }(\Omega ;\mathbb {R}^{d\times d})$$ A = ( a ij ) ∈ L loc ∞ ( Ω ; R d × d ) is a symmetric and locally uniformly positive definite matrix. The potential V lies in a certain local Morrey space (depending on p ) and has a Fuchsian-type isolated singularity at $$\zeta $$ ζ .