On the general Toda system with multiple singular points

Abstract

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} -Δw_i=\sum_{j=1}^na_{i,j}e^{2w_j}+2π\sum_{\ell=1}^mβ_{i,\ell}δ_{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.

17 pages

References in corpus (1)

• Classification and nondegeneracy of $SU(n+1)$ Toda system with singular sources