A LIOUVILLE COMPARISON PRINCIPLE FOR SOLUTIONS OF SINGULAR QUASILINEAR ELLIPTIC SECOND-ORDER PARTIAL DIFFERENTIAL INEQUALITIES

We compare entire weak solutions u and v of quasilinear partial differential inequalities on R-n without any assumptions on their behaviour at infinity and show among other things, that they must coincide if they are ordered, i.e. if they satisfy u >= v in R-n. For the particular case that v 0 we recover some known Liouville type results. Model cases for the equations involve the p-Laplacian operator for p is an element of [1, 2] and the mean curvature operator