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Klein–Gordon–Maxwell–Proca type systems in the electro-magneto-static case: the high dimensional case

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Abstract

We investigate Klein–Gordon–Maxwell–Proca type systems in the context of closed n-dimensional manifolds with \(n \ge 4\). We prove existence of solutions and compactness of the system both in the subcritical and in the critical case.

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Acknowledgements

The authors would like to express their sincere gratitude to the referee for his/her useful comments. The second author is supported by the ANR-BLADE-JC.

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Authors and Affiliations

  1. Département de Mathématiques, Université de Cergy-Pontoise, Site de Saint-Martin, 2 Avenue Adolphe Chauvin, 95302, Cergy-Pontoise Cedex, France

    Emmanuel Hebey

  2. Institut Camille Jordan, Université Claude Bernard Lyon 1, Bâtiment Braconnier, 21 Avenue Claude Bernard, 69622, Villeurbanne Cedex, France

    Pierre-Damien Thizy

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  1. Emmanuel Hebey
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  2. Pierre-Damien Thizy
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Correspondence to Emmanuel Hebey.

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Communicated by A. Chang.

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Hebey, E., Thizy, PD. Klein–Gordon–Maxwell–Proca type systems in the electro-magneto-static case: the high dimensional case. Calc. Var. 58, 116 (2019). https://doi.org/10.1007/s00526-019-1555-7

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