Existence and non-existence results for the SU(3) singular Toda system on compact surfaces

TL;DR

This paper investigates the SU(3) Toda system on compact surfaces, establishing conditions for the existence or non-existence of solutions through variational methods and blow-up analysis.

Contribution

It introduces new geometric inequalities for existence proofs and applies blow-up analysis with Pohozaev identities for non-existence results.

Findings

Existence of solutions under specific parameter conditions

Non-existence results using blow-up analysis

Development of a new geometric inequality

Abstract

We consider the SU(3) Toda system on a compact surface. We give both existence and non-existence results under some conditions on the parameters. Existence results are obtained using variational methods, which involve a geometric inequality of new type; non-existence results are obtained using blow-up analysis and localized Pohozaev identities.