  In this article, we show the existence of a nonnegative solution to the
singular problem $(\mc P_\la)$ posed in a bounded domain $\Omega$ in $\mb R^2$
(see below). We achieve this by approximating the singular function
$u^{-\beta}\log(u)$ by a function $l_\e(u)$ which pointwisely converges to
$-u^\beta\log(u)$ as $\e \ra 0$. Using variational techniques, the perturbed
equation $-\De u+l_\e(u)=\ds\la
\left(\I{\Om}\frac{F(u(y))}{|x-y|^\mu}dy\right)f(u(x))$ is shown to have a
solution $u_\e \in H_0^{1}(\Om)$ when the parameter $\la >0$ is small enough.
Letting $\e \ra 0$ and proving a pointwise gradient estimate, we show that the
solution $u_\e$ converges to a nontrivial nonnegative solution of the original
problem $(\mc P_\la)$.
