Regular traveling waves for a nonlocal diffusion equation

In this paper, we study a nonlocal diffusion equation with a general diffusion kernel and delayed nonlinearity, and obtain the existence, nonexistence and uniqueness of the regular traveling wave solutions for this nonlocal diffusion equation. As an application of the results, we reconsider some models arising from population dynamics, epidemiology and neural network. It is shown that there exist regular traveling wave solutions for these models, respectively. This generalized and improved some results in literatures.