Traveling wave solutions in delayed lattice differential equations with partial monotonicity

In this paper, we investigate a system of delayed lattice differential equations with partial monotonicity. By using Schauder's fixed point theorem, a new cross-iteration scheme is given to establish the existence of traveling wave solutions. Our main results can deal with the existence of traveling wave solution for a class of delayed reaction diffusion system with partial monotonicity and generalize the results of Wu and Zou (J. Differential Equations 135 (1997) 315-357).