In this paper we prove the existence of a nontrivial solution to the nonlinear Schrödinger–Maxwell equations in \mathbb{R}^{3} , assuming on the nonlinearity the general hypotheses introduced by Berestycki and Lions. Résumé: Dans cet article on démontre l'existence d'une solution non-banale et positive pour les équations non-linéaires de Schrödinger–Maxwell dans \mathbb{R}^{3} en supposant que le terme non-linéaire satisfait les hypothèses introduites par Berestycki et Lions.

In this paper we prove the existence of standing wave solutions of nonlinear Schrödinger equation coupled with Maxwell equations which are non-radially symmetric.

We study a class of minimization problems for a nonlocal operator involving an external magnetic potential. The notions are physically justified and consistent with the case of absence of magnetic fields. Existence of solutions is obtained via concentration compactness.