In this paper, we consider a system of nonlinear partial differential
equations modeling the Lotka Volterra interactions of preys and actively moving
predators with prey-taxis and spatial diffusion.
The interaction between predators are modelized
by the statement of a food pyramid condition. We establish the existence of weak
solutions by using Schauder fixed-point theorem and uniqueness via
duality technique. This paper is a generalization of the results
obtained in [2].