On the general Toda system with multiple singular points

2019/04/11 by Ali Hyder, Juncheng Wei, Hyder, Ali +3
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1904.05549

17 pages

arxiv created 2019/04/11 · arxiv updated 2019/04/12

Abstract

In this paper, we consider the following elliptic Toda system associated to a general simple Lie algebra with multiple singular sources \begincases -Δw_i=∑_j=1ⁿa_i,je^2w_j+2π∑_ℓ=1^mβ_i,ℓδ_{p_ℓ} \quadin ℝ²,

w_i(x)=-2log|x|+O(1)~as~|x|→∞, i=1,⋯,n, \endcases 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-Tian's [19] and Hyder-Lin-Wei's [10] results to the general Toda system.

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