Abstract
In this paper we consider the existence of monotone traveling waves for a class of general integral difference models for populations that are dependent on the previous state term and also on long term memory. This allows us to consider multiple past states. For this model we will have to deal with the non-compactness of the evolution operator when we prove the existence of a fixed point. This difficulty will be overcome by using the Monotone Iteration Method and Dini’s Theorem to show uniform convergence of an iterative evolution operator to a continuous wave function.
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