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.