  In this paper we consider a semilinear elliptic equation with a strong
singularity at $u=0$, namely $ \displaystyle u\geq 0 \mbox{ in } \Omega$, $
\displaystyle - div \,A(x) D u = F(x,u) \mbox{ in} \; \Omega$, $u = 0 \mbox{
on} \; \partial \Omega$, with $F(x,s)$ a Carath\'eodory function such that $$
0\leq F(x,s)\leq \frac{h(x)}{\Gamma(s)}\,\,\mbox{ a.e. } x\in\Omega,\, \forall
s>0, $$ with $h$ in some $L^r(\Omega)$ and $\Gamma$ a $C^1([0,+\infty[)$
function such that $\Gamma(0)=0$ and $\Gamma'(s)>0$ for every $s>0$. We
introduce a notion of solution to this problem in the spirit of the solutions
defined by transposition. This definition allows us to prove the existence and
the stability of this solution, as well as its uniqueness when $F(x,s)$ is
nonincreasing in $s$.
