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On the Dirichlet problem for elliptic systems. (English) Zbl 0593.35042
By means of degree theory and results on upper and lower solutions, the authors establish existence and uniqueness for positive solutions of the elliptic system \[ \Delta u+u(a-bu-cv)=0;\quad \Delta v+v(d-eu-fv)=0 \] with positive constants a,...,f.
Reviewer: J.Appell

MSC:
35J45 Systems of elliptic equations, general (MSC2000)
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35B65 Smoothness and regularity of solutions to PDEs
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