Nonnegative solutions of some quasilinear elliptic inequalities and applications

Let f : R → R be a continuous function. It is shown that under certain assumptions on f and A : R → R+ weak C 1 solutions of the differential inequality -div(A(|\nabla u|)\nabla u)\ge f(u) on RN are nonnegative. Some extensions of the result in the framework of subelliptic operators on Carnot groups are considered