EXISTENCE OF FAST POSITIVE SEMI-WAVEFRONT SOLUTIONS TO MONOSTABLE INTEGRO-DIFFERENTIAL EQUATIONS WITH DELAY

We establish the existence of fast positive semi-wavefront solutions to a delay integro-differential problem cu'(t) = J star u(t) + f(u(t - h)), t is an element of R, u(-infinity) = 0, where the asymmetric kernel J is exponentially bounded, the nonlinearity f is an element of C-1([0, +infinity); R) is monostable, h >= 0, and c > 0.