Nicholson’s blowflies equation with a distributed delay

on the occasion of their retirement ABSTRACT. For the Nicholson’s blowflies equation with a distributed delay Z t N(t) ˙ = −δN(t) + p N(s)e h(t) −aN(s) dsR(t, s), t ≥ 0, we obtain existence, positiveness and permanence results for solutions with positive initial conditions. We prove that all nonoscillatory about the positive equilibrium N ∗ solutions tend to N ∗. In the case δ < p < δe there are no slowly oscillating solutions and the positive equilibrium is globally asymptotically stable. Some generalizations to other nonlinear models of population dynamics with a distributed delay in the recruitment term and a nondelayed linear death term are considered