Geodesic
Existence results for nonlinear elliptic equations in bounded domains of \(\mathbb R^n\)
Electronic journal of differential equations, Tome 2006 (2006)
We establish existence results for the boundary-value problem $\Delta u+f(.,u)=0$ in a smooth bounded domain in $\mathbb{R}^n(n\geq 2)$, where $f$ satisfies some appropriate conditions related to a Kato class. The proofs are based on various techniques related to potential theory.
Classification : 34B27, 34J65
Keywords: Green function, elliptic equation, positive solutions 
@article{EJDE_2006__2006__a118,
     author = {Zribi,  Malek},
     title = {Existence results for nonlinear elliptic equations in bounded domains of \(\mathbb {R^n\)}},
     journal = {Electronic journal of differential equations},
     year = {2006},
     volume = {2006},
     zbl = {1128.35344},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a118/}
}
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Zribi,  Malek. Existence results for nonlinear elliptic equations in bounded domains of \(\mathbb R^n\). Electronic journal of differential equations, Tome 2006 (2006). http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a118/