Abstract

We study the travelling wave problemJ {star operator} u - u - c u′ + f (u) = 0 in R, u (- ∞) = 0, u (+ ∞) = 1 with an asymmetric kernel J and a monostable nonlinearity. We prove the existence of a minimal speed, and under certain hypothesis the uniqueness of the profile for c ≠ 0. For c = 0 we show examples of nonuniqueness. © 2007 Elsevier Inc. All rights reserved.