Abstract
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 Schrödinger and the Born–Infeld agrangians, 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.
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A. Azzollini and A. Pomponio are partially supported by a grant of the group GNAMPA of INDAM. A. Pomponio is partially supported also by FRA2016 of Politecnico di Bari. G. Siciliano is supported by Capes, CNPq Grant 305616/2015-3 and Fapesp grant 2016/02617-3, Brazil.
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Azzollini, A., Pomponio, A. & Siciliano, G. On the Schrödinger–Born–Infeld System. Bull Braz Math Soc, New Series 50, 275–289 (2019). https://doi.org/10.1007/s00574-018-0111-y
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DOI: https://doi.org/10.1007/s00574-018-0111-y