Traveling wave solutions for a neutral reaction–diffusion equation with non-monotone reaction

Abstract

In the present paper, we firstly improve the results on traveling wave solution that were established in (Liu and Weng in J. Differ. Equ. 258:3688-3741, 2015) for a neutral reaction-diffusion equation with quasi-monotone reaction. Secondly, by constructing two auxiliary equations and using Schauder's Fixed Point Theorem, we further establish the existence and the asymptotic properties of the traveling wave solution for the equation with non-monotone reaction. Two examples are also given as the application of our results.