On Solutions for Singular Toda System on Riemann Surfaces with Boundary

2024/08/27 by Hu, Zhengni
#35J50 (Primary) 35J61 #35R01 #58J32 (Secondary) #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2408.14979

Abstract

This paper studies solutions to a singular SU(3) Toda system with linear source terms on a compact Riemann surface Σ with smooth boundaries ∂Σ. We establish the existence of solutions when the parameters are not critical, assuming that Euler characteristic χ(Σ)<1 via analyzing the sublevels. Furthermore, we find a sufficient condition that ensures multiple solutions for generic potentials by Morse inequalities and a transversality theorem.

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• Existence and non-existence results for the SU(3) singular Toda system on compact surfaces
• Solutions for Toda systems on Riemann surfaces
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• A continuum of solutions for the SU(3) Toda System exhibiting partial blow-up
• Asymmetric blow-up for the SU(3) Toda System