A global compactness result for a critical nonlinear Choquard equation in RN

This article is concerned with the following class of nonlinear Choquard equations: u + a(x) u = (| x|- mu * | u| 2 * mu)| u| 2 * mu- 2u + q(x)| u| p- 1u, x. RN, u. H1(RN), where 2 * mu = 2N- mu N- 2 is the critical exponent with N = 4 and 0 < mu < N, 1 < p < 2 * - 1 = N+ 2 N- 2, a(x) and q(x) satisfy some assumptions. Through a compactness analysis of the functional corresponding to the above problem, we obtain the existence of weak solutions for this problem under certain assumptions on a(x) and q(x).