Stationary solutions of non-autonomous Maxwell–Dirac systems

Abstract

The Maxwell–Dirac system describes the interaction of a particle with its self-generated electromagnetic field. In this paper, we study the existence of least energy stationary solutions for non-autonomous Maxwell–Dirac system with a nonlinear term in (3+1)-Minkowski space–time via variational methods. This problem is strongly indefinite and presents a lack of compactness. To overcome these difficulties, we will use the linking and concentration compactness arguments.