Multiple solutions to a magnetic nonlinear Choquard equation

We consider the stationary nonlinear magnetic Choquard equation (-i del + A(x))(2)u + V(x)u = (1/|x|(alpha) * |u|(p-2)u, x is an element of R-N where A is a real-valued vector potential, V is a real-valued scalar potential, N >= 3, alpha is an element of (0, N) and 2 - (alpha/N) < p < (2N - alpha)/(N - 2). We assume that both A and V are compatible with the action of some group G of linear isometries of RN. We establish the existence of multiple complex valued solutions to this equation which satisfy the symmetry condition. u(gx) = tau(g)u(x) for all g is an element of G, x is an element of R-N, where tau : G -> S-1 is a given group homomorphism into the unit complex numbers.