An iterative method for non-autonomous nonlocal reaction-diffusion equations

In this paper we provide a method to prove the existence of weak solutions for a type of non-autonomous nonlocal reaction-diffusion equations. Due to the presence of the nonlocal operator in the diffusion term, we cannot apply the Monotonicity Method directly. To use it, we build an auxiliary problem with linear diffusion and later, through iterations and compactness arguments, we show the existence of solutions for the nonlocal problem.