Solitons in Schrodinger-Maxwell equations

In this paper we study the nonlinear Schrodinger-Maxwell equations (NSM). We are interested in analyzing the existence of solitons, namely the existence of finite energy solutions which exhibit stability properties. This paper is divided into two parts. In the first part, we give an abstract definition of solitons and we develop an abstract existence theory. In the second, we apply this theory to NSM.