A population dynamics model with nonautonomous past

In this paper we study a two-phase population model, which distinguishes the population by two different stagesBy the standard technique of characteristics, this population equation is transformed as the ordinary differential equation with nonautonomous pastwhere 1 ≤ p < ∞ and I = [−r, 0] (finite delay) or I = (−∞, 0] (infinite delay), E a Banach space, Φ : W1,p(I, E) → E a linear delay operator and B a nonlinear operator on E. The main result of this paper is the well-posedness of this delay equation by using the (right) multiplicative perturbation result of Desch and Schappacher in [8].