Geodesic
Existence and asymptotic behaviour of positive solutions for semilinear elliptic systems in the Euclidean plane
Electronic journal of differential equations, Tome 2011 (2011)
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.
Classification : 34B27, 35J45, 45M20
Keywords: Green function, semilinear elliptic systems, positive solution 
@article{EJDE_2011__2011__a17,
     author = {Ghanmi,  Abdeljabbar and Toumi,  Faten},
     title = {Existence and asymptotic behaviour of positive solutions for semilinear elliptic systems in the {Euclidean} plane},
     journal = {Electronic journal of differential equations},
     year = {2011},
     volume = {2011},
     zbl = {1229.35057},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a17/}
}
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%A Toumi,  Faten
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Ghanmi,  Abdeljabbar; Toumi,  Faten. Existence and asymptotic behaviour of positive solutions for semilinear elliptic systems in the Euclidean plane. Electronic journal of differential equations, Tome 2011 (2011). http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a17/