Electron. J. Diff. Equ., Vol. 2011 (2011), No. 79, pp. 1-9.

Existence and asymptotic behaviour of positive solutions for semilinear elliptic systems in the Euclidean plane

Abdeljabbar Ghanmi, Faten Toumi

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.

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Abdeljabbar Ghanmi
Département de Mathématiques
Faculté des Sciences de Tunis
Campus Universitaire, 2092 Tunis, Tunisia
email: ghanmisl@yahoo.fr
Faten Toumi
Département de Mathématiques
Faculté des Sciences de Tunis
Campus Universitaire, 2092 Tunis, Tunisia
email: faten.toumi@fsb.rnu.tn

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