  In this paper we consider semilinear elliptic equations with singularities,
whose prototype is the following \begin{equation*} \begin{cases} \displaystyle
- div \,A(x) D u = f(x)g(u)+l(x)& \mbox{in} \; \Omega,\\ u = 0 & \mbox{on} \;
\partial \Omega,\\ \end{cases} \end{equation*} where $\Omega$ is an open
bounded set of $\mathbb{R}^N,\, N\geq 1$, $A\in L^\infty(\Omega)^{N\times N}$
is a coercive matrix, $g:[0,+\infty)\rightarrow [0,+\infty]$ is continuous, and
$0\leq g(s)\leq {{1}\over{s^\gamma}}+1$ $\forall s>0$, with $0<\gamma\leq 1$
and $f,l \in L^r(\Omega)$, $r={{2N}\over{N+2}}$ if $N\geq 3$, $r>1$ if $N=2$,
$r=1$ if $N=1$, $f(x), l(x)\geq 0$ a.e. $x \in \Omega$.
  We prove the existence of at least one nonnegative solution and a stability
result; moreover uniqueness is also proved if $g(s)$ is nonincreasing or
"almost nonincreasing".
  Finally, we study the homogenization of these equations posed in a sequence
of domains $\Omega^\epsilon$ obtained by removing many small holes from a fixed
domain $\Omega$.
