Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 79, pp. 1-9.

Title: Existence and asymptotic behaviour of positive solutions for semilinear
       elliptic systems in the Euclidean plane
       
Authors: Abdeljabbar Ghanmi (Faculte des Sciences de Tunis, Tunisia)
         Faten Toumi  (Faculte des Sciences de Tunis, Tunisia)

Abstract: 
 We study the semilinear elliptic system
 $$
 \Delta u=\lambda p(x)f(v),\Delta v=\lambda q(x)g(u),
 $$
 in an unbounded domain D in $ \mathbb{R}^2$ with compact
 boundary subject to some Dirichlet conditions. We give existence
 results according to the monotonicity of the nonnegative
 continuous functions f and g. The potentials p and q are
 nonnegative and required to satisfy some hypotheses related on a
 Kato class.
 
Submitted March 31, 2011. Published June 20, 2011.
Math Subject Classifications: 34B27, 35J45, 45M20.
Key Words: Green function; semilinear elliptic systems;
           positive solution.