Ground state solutions for a class of Schrödinger–Poisson–Slater equation with Coulomb–Sobolev critical exponent

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This paper is concerned with the Schrödinger–Poisson–Slater equation involving the Coulomb–Sobolev exponent. We apply the concentration compactness principle and the Pohožaev-type identity to overcome loss of compactness caused by the Coulomb exponent and obtain a ground state solution, which generalizes and improves some recent results in the literature.