Non-simple blow-up for singular Liouville equations in unit ball

We investigate the existence of blowing-up solutions to the following singular Liouville problem -Delta u = lambda V)(lambda)(|x|)e(u) - 4 pi N delta(0) in B-1, u = 0 on partial derivative B1, where B-1 is the unit ball in R-2 centered at the origin, V-lambda(|x|) is a positive smooth potential, N is a positive integer (N >= 1), delta(0) defines the Dirac measure with pole at 0, and lambda > 0 is a small parameter. If the potential V-lambda|x|) satisfies some suitable assumptions in terms of the first 2(N + 1) derivatives at 0, then we find a solution which exhibits a non -simple blow-up profile as lambda -> 0(+).