Geodesic
Existence and asymptotic behaviour of positive solutions for semilinear elliptic systems in the Euclidean plane
Electronic Journal of Differential Equations, Tome 2011 (2011).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 
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     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},
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     volume = {2011},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a17/}
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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/