Traveling waves for monotone or non-monotone equations with nonlocal delays in a cylinder

摘要

This paper is devoted to the study of mono-stable and bistable traveling waves for monotone or non-monotone equations with nonlocal time delays in a cylinder. When the time delay is finite, the existence of the traveling wave solutions is established by appealing to the theory of monotone semi-flows for the monotone equation and the fixed point theory coupled with upper-lower solutions method for the non-monotone equation. When the time delay is infinite, the finite-delay approximations method is used to obtain the existence of the traveling waves. (C) 2019 Elsevier Ltd. All rights reserved.