On the general Toda system with multiple singular points (Q2192937)

The authors analyse the solvability of the elliptic Toda system \[ \left\{ \begin{array}{lll} -\Delta w_i=\sum_{j=1}^n a_{i,j} e^{2w_j} + 2\pi\sum_{\ell=1}^m \beta_{i,\ell} \delta_{p_\ell} \quad&\mbox{in}\quad\mathbb{R}^2,\\ w_i(x)=-2\log|x|+O(1)~~\mbox{as}~~|x|\to\infty,\quad &i=1, \ldots, n \end{array} \right. \] associated to general simple Lie algebras with multiple singular sources (and where conditions are impossed on \(\beta_{i,\ell}\in[0,1)\)).