A priori estimates, positivity results, and nonexistence theorems for quasilinear degenerate elliptic inequalities

摘要

A priori bounds for solutions of a wide class of quasilinear degenerate elliptic inequalities are proved. As an outcome we deduce sharp Liouville theorems. Our investigation includes inequalities associated to p-Laplacian and the mean curvature operators in Carnot groups setting. No hypotheses on the solutions at infinity are assumed. General results on the sign of solutions for quasilinear coerciveoncoercive inequalities are considered. Related applications to population biology and chemical reaction theory are also studied.