Abstract: We consider a Liouville type equation in two dimensional domains which arises from prescribing Gaussian curvature problem, the mean filed limit of vortices in Euler flows and limit cases of Chern-Simons models. The “total mass”, which equals the integral of the nonlinear term, plays a key role for this equation. The solutions can blow up when the total mass tends to some critical values. We will discuss how the delta functions in the source term affect the blowup behavior of the solutions and present a formula of the Leray-Schauder degree for the problem.