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

Ramzi Alsaedi

Abstract and Applied Analysis, 2012, vol. 2012, issue 1

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).

Date: 2012
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https://doi.org/10.1155/2012/273017

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:273017

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