Positive Solutions for Some Nonlinear Elliptic Systems in Exterior Domains of â„ 2

Ramzi Alsaedi

Abstract and Applied Analysis, 2012, vol. 2012, 1-13

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 Δ ð ‘¢ = ð ‘ ( ð ‘¥ ) ð ‘¢ ð ›¼ ð ‘£ ð ‘Ÿ , Δ ð ‘£ = ð ‘ž ( ð ‘¥ ) ð ‘¢ ð ‘ ð ‘£ ð ›½ in an exterior domain ð · of â„ 2 , subject to some Dirichlet conditions, where ð ›¼ ≥ 1 , ð ›½ ≥ 1 , ð ‘Ÿ ≥ 0 , ð ‘ â‰¥ 0 and the potentials ð ‘ , ð ‘ž are nonnegative and satisfy some hypotheses related to the Kato class ð ¾ ( ð · ) .

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:273017

DOI: 10.1155/2012/273017

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