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

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.