A predator-prey system with L data

In this paper, we are concerned with a system of nonlinear partial differential equations modeling a predator-prey system in heterogeneous habitats. Preys are assumed to follow a logistic growth in the absence of predation, and predators are assumed to feed on preys with a Holling type II functional response to prey density. Also, interactions between predators are modelized by the statement of a food pyramid condition. Assuming no-flux boundary conditions and L¹ data, we prove the existence of at least one weak solution.