Existence of ground state solutions to Dirac equations with vanishing potentials at infinity

TL;DR

This paper investigates the existence of ground-state solutions for Dirac equations with potentials that vanish at infinity, using variational methods and conditions to address compactness issues.

Contribution

It introduces a novel approach employing minimization over a generalized Nehari set to establish existence results for such Dirac equations.

Findings

Existence of ground-state solutions under specified potential conditions

Overcoming lack of compactness with new conditions on potentials

Application of variational methods to Dirac equations with vanishing potentials

Abstract

In this work we study the existence of ground-state solutions of Dirac equations with potentials which are allowed to vanish at infinity. The approach is based on minimization of the energy functional over a generalized Nehari set. Some conditions on the potentials are given in order to overcome the lack of compactness.