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

Q-curvature Flow for GJMS Operators with Non-trivial Kernel