Liouville theorems for anisotropic quasilinear inequalities

The purpose of this paper is to prove some nonexistence results for nonnegative weak solutions of differential inequalities Lu≥uq,or−Lu≥uq,or−Lu≥0,on RN. Here LL is a quasilinear operator belonging to a wide class of operators, including the anisotropic pseudo-mm-Laplacian operator, the mm-Laplacian operator, the mean curvature operator acting in Euclidean setting, as well as their counterparts in Carnot groups setting.