 Solution

At the stated threshold the idealized system admits a self-sustaining neutron mode. Production and losses balance without the external source. A nonzero continuing source then makes the assumed linear, time-independent response singular rather than selecting a finite equilibrium amplitude.

An apparent infinite steady flux is therefore a failure of that steady linear approximation at the threshold, not a physical prediction that an actual neutron population instantly becomes infinite. Time dependence and feedback must be considered to discuss subsequent behaviour.