A non-monotone time-delayed lattice equation in discrete periodic habitat is concerned. As a fundamental step, a principle eigenvalue problem is introduced, which viewed as a function on a parameter is proved to be strictly convex, piecewise monotone and positive. With the help of such properties, the existence of pulsating waves is obtained by first constructing super and sub solutions, then using Schauder’s fixed-point theorem and finally appealing limiting arguments. The spreading speed and its variational characterization by principle eigenvalue is established by comparison argument. It turns out that the minimal wave speed of pulsating waves coincides with the spreading speed.

研究了离散周期生境中的非单调时滞格子方程。作为基本步骤，引入了一个原理特征值问题，将其视为参数上的函数被证明是严格凸的、分段单调的和正的。借助这些性质，首先构造超解和子解，然后使用 Schauder 不动点定理，最后采用吸引人的极限论证，从而获得脉动波的存在性。通过比较论证建立了传播速度及其主特征值的变分表征。事实证明，脉动波的最小波速与传播速度一致。