Nonlocal problems with Hardy–Littlewood–Sobolev critical exponent and Hardy potential

We are concerned with a Brezis–Nirenberg-type problem for a critical Choquard equation, in the sense of Hardy–Littlewood–Sobolev inequality, and with the Hardy potential in a smooth bounded domain. By exploiting variational methods, we obtain existence results, which extend to different perturbation terms. Some estimates of independent interest about a nonlocal minimization problem are also derived.