Liouville theorems for elliptic inequalities and applications

In this paper we prove nonexistence of positive C-2 solutions for systems o f semilinear elliptic inequalities, for polyharmonic semilinear inequalitie s in cones and, under better conditions on the nonlinearity, for bounded po sitive solutions of elliptic semilinear equations in half spaces. Using a b low-up argument. these results allow us to prove a-priori bounds for a clas s of semilinear elliptic systems of equations in bounded domains.