Convergence for a Liouville equation

In this paper, we study the asymptotic behavior of solutions of the Dirichl et problem for the Liouville equation -Deltau = lambda K(x)e(u)/integral (Omega) K(x)e(u) on a bounded smooth domain Omega in the plane as lambda --> 8m pi, where m = 1, 2,.... The equation is also called the Mean Field Equation in Statisti cal Mechanics. By a result of H.Brezis and F.Merle, any solution sequence m ay have a finite number of bubbles. We give a necessary condition for the l ocation of the bubble points.