Positive Solutions for Some Nonlinear Elliptic Systems in Exterior Domains of

Abstract

Using some potential theory tools and the Schauder fixed point theorem, we prove the existence of positive continuous solutions with a precise global behavior for the competitive semilinear elliptic system , in an exterior domain of , subject to some Dirichlet conditions, where , , , and the potentials are nonnegative and satisfy some hypotheses related to the Kato class .