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, del u)) + f(1)(u) - f(2)(u) = 0 in all R-N. We obtain Liouville type boundedness for the solutions. We show that vertical bar u vertical bar <= (alpha/beta)1/m-q+1 on R-N, under the assumptions f(1)(u) <= alpha u(q-1) and f(2)(u) >= beta u(m), for some 0 < alpha <= beta and m > q - 1 > 0. If u does not change the sign, we prove that u is constant. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4753979]