Positive Solutions for Some Nonlinear Elliptic Systems in Exterior Domains of ℝ2

Abstract EN

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 Δu=p(x)uαvr, Δv=q(x)usvβ in an exterior domain D of R2, subject to some Dirichlet conditions, where α≥1, β≥1, r≥0, s≥0 and the potentials p,q are nonnegative and satisfy some hypotheses related to the Kato class K(D).