In this paper, we consider a class of Fisher–KPP equations with delays appearing in both diffusion and reaction terms. By employing some differential inequality analyses, we prove that the delayed Fisher–KPP equation possesses a pair of quasi-upper and quasi-lower solutions which have absolutely continuous derivatives. Based on this, we apply the monotone iteration method and the Perron’s theorem to establish a sufficient criterion ensuring the existence of wave fronts. Our proof corrects the previous related research.

中文翻译：

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一类延迟 Fisher-KPP 方程的波前


在本文中，我们考虑了一类延迟在扩散和反应项中都出现的 Fisher-KPP 方程。通过采用一些差分不等式分析，我们证明了延迟 Fisher-KPP 方程具有一对具有绝对连续导数的准上解和准下解。基于此，我们应用单调迭代法和 Perron 定理建立了一个充分的准则来保证波前的存在。我们的证明纠正了之前的相关研究。