Electron. J. Diff. Eqns., Vol. 2006(2006), No. 92, pp. 1-11.

Existence results for nonlinear elliptic equations in bounded domains of $R^n$

Malek Zribi

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.

Submitted May 4, 2006. Published August 15, 2006.
Math Subject Classifications: 34B27, 34J65.
Key Words: Green function; elliptic equation; positive solutions.

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Malek Zribi
Département de Mathématiques
Faculté des Sciences de Tunis
Campus universitaire, 1060 Tunis, Tunisia
email: malek.Zribi@insat.rnu.tn

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