On the existence of blowing-up solutions for a mean field equation (Q1775906)

In this paper we construct single and multiple blowing-up solutions to the mean field equation: \[ \begin{cases} - \Delta u = \lambda {{V(x)e^u } \over {\int_\Omega V(x)e^u } }& \text{in }\Omega, \\ u=0 & \text{on } \partial \Omega,\end{cases} \] where \(\Omega\) is a smooth bounded domain in \(\mathbb{R}^2\), \(V\) is a smooth function positive somewhere in \(\Omega\) and \(\lambda\) is a positive parameter.