Stationary periodic solutions to Nonlinear Dirac equations with non-coercive potentials

TL;DR

This paper establishes the existence of stationary periodic solutions to nonlinear Dirac equations on a three-dimensional torus, overcoming challenges posed by non-coercive nonlinearities through perturbation techniques.

Contribution

It introduces a novel approach to handle non-coercive nonlinearities in Dirac equations by employing coercive perturbations and uniform estimates.

Findings

Existence of nontrivial periodic solutions demonstrated.

Uniform bounds obtained for solutions and critical levels.

Method applicable to equations with non-coercive nonlinear terms.

Abstract

We obtain periodic solutions for nonlinear Dirac equations with a nonlinear term that is not necessarily coercive.This amounts to study the equation on a three-dimensional torus.The Palais-Smale condition is enhanced by involving a coercive perturbation.Uniform estimates for the critical levels as well as the Sobolev norms for the perturbed solutions are obtained, making it possible to pass to a limit which gives a nontrivial solution.