Traveling wavefronts for the discrete fisher′s equation

Abstract

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 u ·n = d(Un-1 - 2un + un+1) + f(hook)(un), n ∈ Z, where d is a positive number and f(hook) denotes a Lipschitz continuous function satisfying f(hook)(0) = f(hook)(1) = 0 and f(hook)(x) > 0 for 0 < x < 1. The results are sharp if f(hook) is differentiable at 0 and satisfies f(hook)′(0) x ≥ f(hook)(x) for x > 0. © 1993 by Academic Press, Inc.