Nonlinear Liouville theorems and a priori estimates for indefinite superlinear elliptic equations

Abstract

We establish two general nonlinear Liouville theorems for equations of the type $$ -\Delta u=h(x_1)f(u),\; u\geq 0 \; \mbox{ in } R^N,\; \sup_{R^N}u < +\infty. $$ We then show how these Liouville theorems can be used to obtain a priori estimates for positive solutions of indefinite superlinear elliptic equations for several new cases left open in previous research.