Abstract

We consider the Hénon-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 < m + 1 and give partial results for higher dimensions.