where rho > 0, V-1, V-2 > 0 are smooth potentials in Omega, tau > 0, Omega is a smooth bounded domain in R-2 and B(xi(i), epsilon(i)) is a ball centered at xi(i) is an element of Omega with radius epsilon(i) > 0, i = 1,..., m. When rho > 0 is small enough and m(1) is an element of{1,..., m - 1}, there exist radii epsilon = (epsilon(1),..., epsilon(m)) small enough such that the problem has a solution which blows-up positively at the points xi(1),..., xi(m1) and negatively at the points xi(m1+1),..., xi(m) as rho -> 0. The result remains true in cases m(1) = 0 with V-1 = 0 and m(1) = m with V-2 = 0, which are Liouville type equations.