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 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).
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