Abstract
This paper is devoted to studying the existence and nonexistence of traveling wave solution for a nonlocal dispersal delayed predator-prey system with the Beddington-DeAngelis functional response and harvesting. By constructing the suitable upper-lower solutions and applying Schauder's fixed point theorem, we show that there exists a positive constant $c^*$ such that the system possesses a traveling wave solution for any given $c> c^*$. Moreover, the asymptotic behavior of traveling wave solution at infinity is obtained by the contracting rectangles method. The existence of traveling wave solution for $c=c^*$ is established by means of Corduneanu's theorem. The nonexistence of traveling wave solution in the case of $c<c^*$ is also discussed.
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