Rabinowitz-Floer Homology for Super-quadratic Dirac Equations On Compact spin Manifolds

TL;DR

This paper develops Rabinowitz-Floer homology for super-quadratic Dirac equations on compact spin manifolds, providing new existence results for solutions with various nonlinearities.

Contribution

It introduces a novel homology framework for super-quadratic Dirac equations, enabling the derivation of existence results for solutions on spin manifolds.

Findings

Established Rabinowitz-Floer homology groups for the problem

Proved existence of solutions for sub-critical nonlinearities

Extended results to critical nonlinearities

Abstract

In this paper we investigate the properties of a semi-linear problem on a spin manifold involving the Dirac operator, through the construction of Rabinowitz-Floer homology groups. We give several existence results for sub-critical and critical non-linearities as application of the computation of the different homologies.