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(3) Toda system with multiple singular sources:

Δw1 = 2e2w1 e2w2 + 2π =1mβ 1,δP in 2,  (1) Δw2 = 2e2w2 e2w1 + 2π =1mβ 2,δP in 2, wi(x) = 2log|x| + O(1) as |x|;i = 1,2,  (2)

with m 3 and βi, [0,1). We prove existence and nonexistence results under suitable assumptions on βi,. This generalizes Luo–Tian’s (1992) result for a singular Liouville equation in 2. We also study existence results for a higher order singular Liouville equation in 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