Consider the class of lattice ordinary differential equations
with , , . The goal is to prove the existence of a travelling wave solution to (*) with wave speed : , where is differentiable and satisfies , . The authors establish such type of solution for and by the method of monotone iteration (lower and upper solutions). The case is treated by using the method of B. Zinner, G. Harris and W. Hudson [J. Differ. Equations 105, No. 1, 46–62 (1993; Zbl 0778.34006)].