Traveling Wavefronts for the Discrete Fisher′s Equation

Using continuation and comparison methods we obtain conditions for the existence and nonexistence of traveling wavefronts with speed c of the discrete Fisher′s equation where d is a positive number and ƒ denotes a Lipschitz continuous function satisfying ƒ(0) = ƒ(1) = 0 and ƒ(x) > 0 for 0 < x < 1. The results are sharp if ƒ is differentiable at 0 and satisfies ƒ′(0) x ≥ ƒ(x) for x > 0.