B2 and G2 Toda systems on compact surfaces: a variational approach

TL;DR

This paper studies B2 and G2 Toda systems on compact surfaces, employing variational methods to establish existence and multiplicity of solutions under certain topological and parameter conditions, and extends results to general systems.

Contribution

It introduces a variational approach to analyze B2 and G2 Toda systems on compact surfaces, proving new existence and multiplicity results and generalizing to broader systems.

Findings

Existence of solutions under topological assumptions

Multiple solutions under generic parameter conditions

Extension of results to general Toda systems

Abstract

We consider the B2 and G2 Toda systems on compact surfaces. We attack the problem using variational techniques. We get existence and multiplicity of solutions under a topological assumption on the surface and some generic conditions on the parameters. We also extend some of the results to the case of general systems.