  We are concerned with the existence of blowing-up solutions to the following
boundary value problem $$-\Delta u= \la a(x) e^u-4\pi N \delta_0\;\hbox{ in }
\Omega,\quad u=0 \;\hbox{ on }\partial \Omega,$$ where $\Omega$ is a smooth and
bounded domain in $\R^2$ such that $0\in\Omega$, $a(x)$ is a positive smooth
function, $N$ is a positive integer and $\la>0$ is a small parameter. Here
$\delta_0$ defines the Dirac measure with pole at $0$. We find conditions on
the function $a$ and on the domain $\Omega$ under which there exists a solution
$u_\la$ blowing up at $0$ and satisfying $\la\into a(x)e^{u_\la} \to 8\pi(N+1)$
as $\la\to 0^+$.
