School of Mathematics and Physics, University of Science & Technology Beijing, Beijing 100083, China.
School of Mathematical and Statistical Sciences, University of Texas Rio Grande Valley, Edinburg, Texas 78539, USA.
Math Biosci Eng. 2021 Feb 2;18(2):1629-1652. doi: 10.3934/mbe.2021084.
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.
这篇论文致力于研究一类具有 Beddington-DeAngelis 功能性反应和收获的非局部扩散时滞捕食-被捕食系统的行波解的存在性与不存在性。通过构造合适的上下解，并运用 Schauder 不动点定理，我们证明了对于任意给定的 $c>c^$，系统存在一个正的常数 $c^$使得系统存在行波解。此外，通过收缩矩形方法得到了行波解在无穷远处的渐近行为。利用 Corduneanu 定理证明了 $c=c^$ 时行波解的存在性。还讨论了 $c<c^$ 时行波解不存在的情况。
