#### Vol. 305, No. 2, 2020

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The SU$(3)$ Toda system with multiple singular sources

### Ali Hyder, Changshou Lin and Juncheng Wei

Vol. 305 (2020), No. 2, 645–666
DOI: 10.2140/pjm.2020.305.645
##### Abstract

We consider the singular SU$\left(3\right)$ Toda system with multiple singular sources:

with $m\ge 3$ and ${\beta }_{i,\ell }\in \left[0,1\right)$. We prove existence and nonexistence results under suitable assumptions on ${\beta }_{i,\ell }$. This generalizes Luo–Tian’s (1992) result for a singular Liouville equation in ${ℝ}^{2}$. We also study existence results for a higher order singular Liouville equation in ${ℝ}^{n}$.

##### Keywords
Toda system, blow-up analysis
##### Mathematical Subject Classification 2010
Primary: 35B40, 35B44, 35J61
##### Milestones
Received: 13 March 2019
Revised: 19 May 2019
Accepted: 11 October 2019
Published: 29 April 2020
##### Authors
 Ali Hyder Department of Mathematics Johns Hopkins University Baltimore, MD United States Changshou Lin Department of Mathematics, Taida Institute of Mathematical Sciences National Taiwan University Taipei Taiwan Juncheng Wei Department of Mathematics University of British Columbia Vancouver BC Canada