Ground state solutions for Choquard equations with Hardy potentials and critical nonlinearity

We are concerned with discussing the ground state solutions of the Choquard equation with the Hardy potentials and critical Sobolev exponent: {-Delta u + (a - mu/vertical bar x vertical bar(2)) u = (I-alpha * F(u))f(u) + vertical bar u vertical bar(2*-2) u, X is an element of R-N \ {0}, u subset of H-1(R-N), where N >= 3, alpha is an element of (0, N), 0 <= mu < <(mu)over bar> := (N-2)(2)/4, I-alpha is the Riesz potential, 2* := 2N/(N - 2) is the critical Sobolev exponent, and f. C(R, R) satisfies neither the usual Ambrosetti-Rabinowitz type condition nor any monotonicity condition. Using some new variational and analytic techniques, we obtain a ground state solution of Poho. z aev type for the given problem.