New methods for the existence and uniqueness of traveling waves of non-monotone integro-difference equations with applications

A class of non-monotone integro-difference equations are investigated. It is shown that the spreading speed coincides with the minimal wave speed, as well as the uniqueness of traveling waves up to translations. Our methods are different from those in [7,12] and rely on the priori estimate of the decay speed of wave profile and allow (i) to deal with the iterative map without compactness; (ii) to incorporate the critical case which corresponds to the slowest wavefronts into consideration; (iii) to weaken or to remove various restrictions on kernels and nonlinearities. Finally, these results are applied to some population models. (C) 2019 Elsevier Inc. All rights reserved.