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We investigate a predator-prey model for egg-eating predat ors in which the prey population is assumed to have an age structure. By the method of characteristics, this model red uc s to a system of integral equations. Then a generalizatio n of the Banach fixed-point theorem is used to show, under relatively mild co nditions, the existence of a unique, global, weak solution t o the population problem. Furthermore, this methodology allows us to genera te a sequence of iterates, called the Picard iterates, that c onverges to the solution. Also, we strengthen the assumptions of the exi stence-uniqueness theorem to establish the validity of the corresponding conservation law in integral form. Thus we prove a result whi ch shows the coexistence of both predator and prey species ov er a long time.

Egg-eating predators in interaction with age-structured prey population