Existence and uniqueness of solutions for single-population   McKendrick-von Foerster models with renewal
  We study a McKendrick-von Foerster type equation with renewal. This model is represented by a single equation which describes one species which produces young individuals. The renewal condition is linear, but takes into account some history of the population. This model addresses nonlocal interactions between individuals structured by age. The vast majority of size-structured models are also treatable. Our model generalizes a number of earlier models with delays and integrals. The existence and uniqueness is proved through a fixed-point approach to an equivalent integral problem in $L^{\infty}\cap L^1.$ 
Agnieszka Bart{\l}omiejczyk, Henryk Leszczy\'nski, Piotr Zwierkowski
math.AP