On the general Toda system with multiple singular points

In this paper, we consider the following elliptic Toda system associated to any general simple Lie algebra with multiple singular sources - Δ w i = ∑ j = 1 n a i , j e 2 w j + 2 π ∑ ℓ = 1 m β i , ℓ δ p ℓ in R 2 , w i ( x ) = - 2 log | x | + O ( 1 ) as | x | → ∞ , i = 1 , … , n , where β i , ℓ ∈ [ 0 , 1 ) . Under some suitable assumption on β i , ℓ we establish the existence and non-existence results. This paper generalizes Luo and Tian’s (Proc Am Math Soc 116(4):1119–1129, 1992) and Hyder et al. (Pac J Math 305(2):645–666, 2020) results to the general Toda system.