Min-max solutions for super sinh-Gordon equations on compact surfaces

TL;DR

This paper develops a variational approach to find min-max solutions for super sinh-Gordon equations on compact surfaces, providing the first non-trivial solutions of this type and analyzing their multiplicity using symmetry.

Contribution

It introduces a novel variational framework and linking argument to establish min-max solutions for super sinh-Gordon systems on compact surfaces.

Findings

First non-trivial min-max solutions for super sinh-Gordon equations

Use of linking argument and Nehari manifold in analysis

Multiplicity results based on problem symmetry

Abstract

In the present paper we initiate the variational analysis of a super sinh-Gordon system on compact surfaces, yielding the first example of non-trivial solution of min-max type. The proof is based on a linking argument jointly with a suitably defined Nehari manifold and a careful analysis of Palais-Smale sequences. We complement this study with a multiplicity result exploiting the symmetry of the problem.