Vortex-type solutions to a magnetic nonlinear Choquard equation

We consider the stationary nonlinear magnetic Choquard equation where is a magnetic potential and is a bounded electric potential. For a given group of linear isometries of , we assume that A(gx) = gA(x) and W(gx) = W(x) for all . Under some assumptions on the decay of A and W at infinity, we establish the existence of solutions to this problem which satisfy where is a given continuous group homomorphism into the unit complex numbers.