AbstractWe consider the Liouville equation−Δu = λeu in Ω, u =0 on∂Ω,on a smooth bounded domain Ω in ℝfor m ∈ℕ. We prove that the number of blow up points m is less than or equal to the Morse index of uAs a corollary, we show that if a solution u
Multiple Blow-Up Solutions for the Liouville Equation with Singular Data