On the Schr\"odinger-Born-Infeld system

In this paper we study a system which we propose as a model to describe the interaction between matter and electromagnetic field from a dualistic point of view. This system arises from a suitable coupling of the Schr\"odinger and the Born-Infeld lagrangians, this latter replacing the role that, classically, is played by the Maxwell lagrangian. We use a variational approach to find an electrostatic radial ground state solution by means of suitable estimates on the functional of the action.