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 coercive/noncoercive inequalities are considered. Related applications to population biology and chemical reaction theory are also studied.
