  We investigate the prescribed Q-curvature flow for GJMS operators with
non-trivial kernel on compact manifolds of even dimension. When the total
Q-curvature is negative, we identify a conformally invariant condition on the
nodal domains of functions in the kernel of the GJMS operator, allowing us to
prove the global existence and the convergence of the flow to a metric which is
conformal to the initial one, and having a prescribed Q-curvature. If the total
Q-curvature is positive, we show that the flow blows up in finite time.
