Positive solutions for some nonlinear elliptic systems in exterior domains of ℝ 2

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)u αv r, Δv = q(x)u sv β in an exterior domain D of ℝ 2, 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). Copyright 2012 Ramzi Alsaedi.