Nonlocal anisotropic dispersal with monostable nonlinearity

We study the travelling wave problemJ⋆u−u−cu′+f(u)=0inR,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≠0c≠0. For c=0c=0 we show examples of nonuniqueness.