Uniqueness of fast travelling fronts in reaction-diffusion equations   with delay
  We consider positive travelling fronts of the time-delayed reaction-diffusion equation with the monostable birth function. Our main result says that for every fixed and sufficiently large velocity c, the positive travelling front is unique (modulo translations). To prove the uniqueness, we introduce a small parameter 1/c and realize the Lyapunov-Schmidt reduction in a scale of Banach spaces. 
Maitere Aguerrea, Sergei Trofimchuk, Gabriel Valenzuela