Blowup solutions for a Liouville equation with singular data

We study the existence of multiple blowing up solutions for a semilinear elliptic equation with homogeneous Dirichlet boundary condition, exponential nonlinearity, and a singular source term given by Dirac masses. In particular, we extend the result of Baraket and Pacard [Calc. Var. Partial Differential Equations, 6 (1998), pp. 1–38] by allowing the presence, in the equation, of a weight function possibly vanishing in some points