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On the Schrödinger-Maxwell equations under the effect of a general nonlinear term. (English) Zbl 1187.35231

Summary: 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.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35Q60 PDEs in connection with optics and electromagnetic theory
78A30 Electro- and magnetostatics
35B09 Positive solutions to PDEs
35D30 Weak solutions to PDEs
35A15 Variational methods applied to PDEs
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References:

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