Existence results for a super-Liouville equation on compact surfaces

TL;DR

This paper proves the existence of solutions for a super-Liouville equation on compact surfaces with genus greater than one, using variational methods like min-max, Nehari manifold, and Palais-Smale condition.

Contribution

It provides the first non-trivial existence result for super-Liouville equations on higher genus surfaces employing advanced variational techniques.

Findings

Existence of solutions established via min-max methods.

Application of Nehari manifold and Palais-Smale condition.

Identification of mountain pass or linking geometry in the problem.

Abstract

We are concerned with a super-Liouville equation on compact surfaces with genus larger than one, obtaining the first non-trivial existence result for this class of problems via min-max methods. In particular we make use of a Nehari manifold and, after showing the validity of the Palais-Smale condition, we exhibit either a mountain pass or linking geometry.