Ground states for a zero‐mass and Coulomb–Sobolev critical Schrödinger–Poisson–Slater problem

Abstract In this paper, we consider the following Schrödinger–Poisson–Slater equation: where and . Using the Sobolev critical approximation method and Schwartz symmetrization rearrangements, we obtain the existence of ground state solutions to the above problem. To the best of our knowledge, this is the first study of the existence of ground state solutions on the positive energy level when .