Nonexistence Results for a Singular Quasilinear Anisotropic Equation

We establish the nonexistence of positive stable solutions u ∈ W loc 1 , p ( R N ) to the singular quasilinear anisotropic equation Δ B H u = u − q in R N , where q > 0 , in low dimensions. Under similar assumptions, we further prove that, for the pure Finsler p -Laplacian, there exist no solutions that are stable outside a compact set. The proofs rely on several integral estimates and asymptotic analysis of the solutions.