Electronic Journal of Differential Equations, Vol. 2006(2006),
No. 92, pp. 1-11. Title: Existence results for nonlinear
elliptic equations in bounded domains of $R^n$ Author: Malek
Zribi (Faculte des sciences de tunis, Tunisia) Abstract: 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.