Positive solutions for nonhomogenous Choquard equations involving doubly critical exponents

This paper is concerned with nonhomogenous Choquard equations involving doubly critical exponents. First, we use a fixed point theorem to prove the existence of positive solutions to the above equation under certain assumptions. Then, on the positive solution of the equation, we get the regularity in a bounded domain with estimating the ‐bounds by Moser's iterative technique.