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doi: 10.3934/dcdss.2022061
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## Traveling wave solutions of periodic nonlocal Fisher-KPP equations with non-compact asymmetric kernel

 Department of Mathematics, University of Louisiana at Laffayette, Lafayette, LA 70504-1010, USA

Received  July 2021 Revised  December 2021 Early access March 2022

This paper deals with front propagation for nonlocal monostable equations in spatially periodic habitats. In the authors' earlier works, assuming the existence of principal eigenvalue, it is shown that there are periodic traveling wave solutions to a spatially periodic nonlocal monostable equation with symmetric and compact kernel connecting its unique positive stationary solution and the trivial solution in every direction with all propagating speeds greater than the spreading speed in that direction. In this paper, first assuming the existence of principal eigenvalue, we extend the results to the case that the kernel is asymmetric and supported on a non-compact region. In addition, without the assumption of the existence of principal eigenvalue, we explore the existence of semicontinuous traveling wave solutions.

Citation: Aijun Zhang. Traveling wave solutions of periodic nonlocal Fisher-KPP equations with non-compact asymmetric kernel. Discrete and Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2022061
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