Multiple positive bound state solutions for a critical Choquard equation

In this paper we consider the problem(P lambda()) {-Delta u + V-lambda(x)u = (I-mu * vertical bar u vertical bar(2 mu*))vertical bar u vertical bar(2 mu*-2)u in R-N,u > 0 in R-N,where V-lambda = lambda + V-0 with lambda >= 0, V-0 is an element of L-N/2(R-N), I-mu = 1/vertical bar x vertical bar(mu) is the Riesz potential with 0 < mu < min{N, 4} and 2(mu)* = 2N-mu/N-2 with N >= 3. Under some smallness assumption on V-0 and lambda we prove the existence of two positive solutions of (P-lambda). In order to prove the main results, we used variational methods combined with degree theory.