Liouville-type theorems for a quasilinear elliptic equation of the H´enon-type

In the paper "Liouville-type theorems for a quasilinear elliptic equation of the H´enon-type", We consider the H´enon-type quasilinear elliptic equation −Δmu = |x| aup where Δmu = div(|∇u| m−2∇u), m > 1, p>m − 1 and a ≥ 0. We are concerned with the Liouville property, i.e. the nonexistence of positive solutions in the whole space RN . We prove the optimal Liouville-type theorem for dimension N