  In this paper, we consider the following elliptic Toda system associated to a
general simple Lie algebra with multiple singular sources \begin{equation*}
\begin{cases} -\Delta
w_i=\sum_{j=1}^na_{i,j}e^{2w_j}+2\pi\sum_{\ell=1}^m\beta_{i,\ell}\delta_{p_\ell}
\quad&\mbox{in}\quad\mathbb{R}^2,\\ \\
w_i(x)=-2\log|x|+O(1)~\mbox{as}~|x|\to\infty,\quad &i=1,\cdots,n, \end{cases}
\end{equation*} where $\beta_{i,\ell}\in[0,1)$. Under some suitable assumption
on $\beta_{i,\ell}$ we establish the existence and non-existence results. This
paper generalizes Luo-Tian's [19] and Hyder-Lin-Wei's [10] results to the
general Toda system.

Analysis of PDEs