Positive Solutions of Quasilinear Elliptic Equations with Fuchsian Potentials in Wolff Class

Using Harnack’s inequality and a scaling argument we study Liouville-type theorems and the asymptotic behaviour of positive solutions near an isolated singular point ζ ∈ ∂ Ω ∪ { ∞ } for the quasilinear elliptic equation - div ( | ∇ u | A p - 2 A ∇ u ) + V | u | p - 2 u = 0 in Ω , where Ω is a domain in R d , d ≥ 2 , 1 < p < d , and A = ( a ij ) ∈ L loc ∞ ( Ω ; R d × d ) is a symmetric and locally uniformly positive definite matrix. It is assumed that the potential V belongs to a certain Wolff class and has a generalized Fuchsian-type singularity at an isolated point ζ ∈ ∂ Ω ∪ { ∞ } .