Differentiability of the age-dependent population system with time delay in the birth process ✩

In this paper, by using semigroup approach, we concerned with the regularity of the age-dependent population system with instantaneous time delay in the birth process. We prove that, under some additional condition, the solution semigroup {T (t), t 0} of the population evolution equation is eventually differentiable, i.e., there exists t0 > 0 such that T (t) is differentiable for t > t0.  2004 Elsevier Inc. All rights reserved.