Positive Solutions of Superlinear Elliptic Equations with Respect to the Schrödinger Operator

We study positive solutions of semilinear elliptic equations with respect to the Schrödinger operator in the superlinear case. In a bounded smooth domain, a priori estimates for solutions and their gradients, the Harnack inequality and the boundary Harnack principle are presented. As applications, we also investigate the asymptotic behavior of positive solutions with isolated boundary singularities and the removability of isolated boundary singularities.