Nonlocal anisotropic dispersal with monostable nonlinearity

We study the travelling wave problem J * u - u - cu' + f(u) = 0 in R, u(-infinity) = 0, u(+infinity) = 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 not equal 0. For c = 0 we show examples of nonuniqueness.(c) 2007 Elsevier Inc. All rights reserved.