Abstract

In this note we are concerned with the strong maximum principle (SMP) and the compact support principle (CSP) for non-negative solutions to quasilinear elliptic inequalities of the formdiv (A (| ? u |) ? u) + G (| ? u |) - f (u) = 0 in O, anddiv (A (| ? u |) ? u) + G (| ? u |) - f (u) = 0 in R N {set minus} B r (0), respectively. We give new conditions on the data (A, G, f) to obtain (SMP) and (CSP). When these conditions are particularized to the m-Laplacian and pure power nonlinearities we completely classify the data according to the validity of the (CSP) or the (SMP). In doing so we clarify the general situation and we consider a case not covered in the literature. © 2008 Elsevier Inc. All rights reserved.