Nonlinear Liouville theorems for Grushin and Tricomi operators

The aim of this paper is to study necessary conditions for existence of weak solutions of the inequality L (x, y, D-x, D-y,) u greater than or equal to \u\(q)/\x\(01)\y\(02), xis an element of R^d, y is an element of R^k where L is a quasi-homogeneous differential operator, q>1, theta(1) .theta(2) is an element of R and k, d greater than or equal to 1. As special cases, our results can be applied when L is Tricomi or Grushin-type operators. (C) 2003 Elsevier Science (USA). All rights reserved