Summary: In this paper Volterra’s population equation with diffusion for a single, isolated species
is considered. Generalizing a result of R. K. Miller
[SIAM J. Appl. Math. 14, 446-452 (1966; Zbl 0161.31901
)] it is shown that every nonnegative solution
, to a spatially homogeneous distribution
, independent of the initial distribution of
. For proof, a recursively defined sequence of pairs of lower and upper solutions is used.