Homogenization of a Dirichlet semilinear elliptic problem with a strong singularity at u=0 in a domain with many small holes
In the present paper we perform the homogenization of the semilinear elliptic problem
\begin{equation*}
\begin{cases}
u^\eps \geq 0 & \mbox{in} \; \oeps,\\
\displaystyle - div \,A(x) D u^\eps = F(x,u^\eps) & \mbox{in} \; \oeps,\\
u^\eps = 0 & \mbox{on} \; \partial \oeps.\\
\end{cases}
\end{equation*}