中文摘要：

该文主要考虑非局部时滞反应扩散方程行波解的存在性．对于特殊的核函数，通过线性链技巧和几何奇异扰动理论有机结合，建立了带有非局部时滞反应扩散方程和对应的不带时滞反应扩散方程行波解存在性之间的自然联系．得到如果不带时滞反应扩散方程行波解存在，则在时滞充分小的条件下对应的带时滞反应扩散方程行波解也存在．

英文摘要：

This paper is concerned with the existence of a reaction-diffusion equation with nonlocal delay. For special kernels, by linear chain trick and geometric singular perturbation theory, the authors consider a natural connection between the existence of travelling wave solutions for the reaction-diffusion equation with nonlocal delay and the existence of travelling wave solutions for the corresponding undelayed reaction-diffusion equation. It is showed that if the corresponding undelayed reaction-diffusion equation has a travelling wave solution, then the reaction-diffusion with nonlocal delay also has a travelling wave solution for any sufficiently small delay.