Geodesic
Existence of positive solutions for some nonlinear elliptic systems on the half space
Electronic journal of differential equations, Tome 2011 (2011)
We prove some existence of positive solutions to the semilinear elliptic system

$\displaylines{ \Delta u =\lambda p(x)g(v)\cr \Delta v =\mu q(x)f(u) }$

in the half space ${\mathbb{R}}^n_+, n\geq 2$, subject to some Dirichlet conditions, where $\lambda$ and $\mu$ are nonnegative parameters. The functions $f, g$ are nonnegative continuous monotone on $(0,\infty)$ and the potentials $p, q$ are nonnegative and satisfy some hypotheses related to the Kato class $K^\infty({\mathbb{R}}^n_+)$.
Classification : 35J55, 35J60, 35J65
Keywords: Green function, Kato class, elliptic systems, positive solutions 
@article{EJDE_2011__2011__a13,
     author = {Zeddini,  Noureddine},
     title = {Existence of positive solutions for some nonlinear elliptic systems on the half space},
     journal = {Electronic journal of differential equations},
     year = {2011},
     volume = {2011},
     zbl = {1221.35140},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a13/}
}
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JO  - Electronic journal of differential equations
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%A Zeddini,  Noureddine
%T Existence of positive solutions for some nonlinear elliptic systems on the half space
%J Electronic journal of differential equations
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Zeddini,  Noureddine. Existence of positive solutions for some nonlinear elliptic systems on the half space. Electronic journal of differential equations, Tome 2011 (2011). http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a13/