Liouville type theorems for nonlinear elliptic equations involving operator in divergence form

The aim of this paper is to study the properties of the solutions of div (A(x,∇u))+f1(u)−f2(u)=0 in all RN. We obtain Liouville type boundedness for the solutions. We show that |u|≤(αβ)1m−q+1 on RN, under the assumptions f1(u) ⩽ αuq–1 and f2(u) ⩾ βum, for some 0 q−1 > 0. If u does not change the sign, we prove that u is constant.