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Existence of Positive Ground State Solutions for Fractional Choquard Systems in Subcritical and Critical Cases

Author

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  • Huiqin Lu

    (School of Mathematics and Statistics, Shandong Normal University, Jinan 250358, China
    Mathematics and Science College, Shanghai Normal University, Shanghai 200234, China)

  • Kexin Ouyang

    (School of Mathematics and Statistics, Shandong Normal University, Jinan 250358, China)

Abstract

We investigate a class of fractional linearly coupled Choquard systems. For the subcritical case and all critical cases, we prove the existence, nonexistence and symmetry of positive ground state solutions of systems, by using the Nehari manifold method, the Pohožaev identity and the Schwartz symmetrization rearrangements. In particular, we overcome the lack of compactness of the critical nonlinearities by using the behaviour of sufficiently small Nehari energy levels.

Suggested Citation

  • Huiqin Lu & Kexin Ouyang, 2023. "Existence of Positive Ground State Solutions for Fractional Choquard Systems in Subcritical and Critical Cases," Mathematics, MDPI, vol. 11(13), pages 1-16, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:13:p:2938-:d:1183757
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