{"paper":{"title":"On the general Toda system with multiple singular points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ali Hyder, Juncheng Wei, Wen Yang","submitted_at":"2019-04-11T06:55:04Z","abstract_excerpt":"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 t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.05549","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}