A variational Analysis of the Toda System on Compact Surfaces

TL;DR

This paper investigates the Toda system on compact surfaces, establishing existence results through variational methods and a novel Moser-Trudinger inequality that accounts for concentration phenomena.

Contribution

Introduces a new Moser-Trudinger type inequality tailored for the Toda system, enabling existence proofs in non-coercive settings on compact surfaces.

Findings

Proved existence of solutions under specific conditions.

Developed a new inequality for the Toda system.

Analyzed concentration behavior of solutions.

Abstract

In this paper we consider the Toda system of equations on a compact surface. We will give existence results by using variational methods in a non coercive case. A key tool in our analysis is a new Moser-Trudinger type inequality under suitable conditions on the center of mass and the scale of concentration of the two components u_1, u_2.