Liouville theorems for stable solutions of p-Laplace equations with convex nonlinearities

We prove a Liouville type theorem for stable solutions of the equation −div(|Du|p−2Du)=f(u)−div(|Du|p−2Du)=f(u) in the whole space RNRN, where f   is a non-negative, non-decreasing and convex function. We apply that result to obtain another Liouville type theorem for non-negative solutions of similar equations in the half-space R+N.