Ground state solutions and decay estimation of Choquard equation with critical exponent and Dipole potential

In this paper, we study a class of Choquard equations with critical exponent and Dipole potential.We prove the existence of radial ground state solutions for Choquard equations by using the refined Sobolev inequality with the Morrey norm, and show that any nonnegative weak solutions of Choquard equations have additional decay properties in terms of ground state representation.