[en] Some peculiarities of neutron density time variation are considered in the system with an external source. Determined are necessary conditions for the neutron source distribution function. Neutron density decreases momotonously with time after a source flash, when these conditions are satisfied. Analogous conditions for the evolution equation with time-independent positive-semidefinite operator are stated. The single-rapidity transport equation for thermal neutrons is considered as a particular case. The effect of the source pulse duration on the value of maximum neutron density in the system is also found