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中文摘要：
本文利用上下解和交叉迭代方法研究一类具有时滞的时间离散反应扩散系统行波解的存在性.所得结果能很好地应用到时间离散的竞争系统{u_n（x）-u_（n-1）（x）=d_1？^2/？x^2u_n（x）＋r_1u_n（x）[1-a_1u_n（x）-b_1u_（n-t1）（x）-c_1u_（n-t2）（x）],u_n（x）-u_（n-1）（x）=d_2？^2/？x^2u_n（x）＋r_2u_n（x）[1-a_2u_n（x）-b_2u_（n-t3）（x）-c_2u_（n-t4）（x）]中,而研究其行波解存在性转化为寻找一对合适的上下解.这些结果推广了已有的一些结果.
英文摘要：
In this paper,we investigate the existence of traveling wave solutions for a temporally discrete reaction-diffusion system with delays by using upper-lower solution methods and a cross iteration scheme.T？he obtained result will be applied to the time discrete competition system{u_n（x）-u_（n-1）（x）=d_1？~2/？x~2u_n（x）＋r_1u_n（x）[1-a_1u_n（x）-b_1u_（n-t1）（x）-c_1u_（n-t2）（x）],u_n（x）-u_（n-1）（x）=d_2？~2/？x~2u_n（x）＋r_2u_n（x）[1-a_2u_n（x）-b_2u_（n-t3）（x）-c_2u_（n-t4）（x）] The existence of traveling waves is reduced to look for a suitable upper-lower solutions.The result in present paper extends some known results.
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