Positive solutions for some competitive elliptic systems

Using some potential theory tools and the Schauder fixed point theorem, we prove the existence of positive bounded continuous solutions with a precise global behavior for the semilinear elliptic system Δ u = p ( x ) u α ν r in domains D of ℝ n , n ≥ 3, with compact boundary (bounded or unbounded) su...

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Bibliographic Details
Published inMathematica Slovaca Vol. 64; no. 1; pp. 61 - 72
Main Authors Alsaedi, Ramzi, Mâagli, Habib, Zeddini, Noureddine
Format Journal Article
LanguageEnglish
Published Heidelberg Versita 01.02.2014
Subjects
Algebra
elliptic systems
Green function
Kato class
Mathematics
Mathematics and Statistics
Maximum principle
positive solutions
Primary 31B35, 35B09, 35B50, 35J08, 35J57
positive solutions
Maximum principle
Primary 31B35, 35B09, 35B50, 35J08, 35J57
elliptic systems
Green function
Kato class
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Summary:Using some potential theory tools and the Schauder fixed point theorem, we prove the existence of positive bounded continuous solutions with a precise global behavior for the semilinear elliptic system Δ u = p ( x ) u α ν r in domains D of ℝ n , n ≥ 3, with compact boundary (bounded or unbounded) subject to some Dirichlet conditions, where α ≥ 1, β ≥ 1, r ≥ 0, s ≥ 0 and the potentials p , q are nonnegative and belong to the Kato class K ( D ).
ISSN:0139-9918
1337-2211
1337-2211
DOI:10.2478/s12175-013-0187-1