  In this paper, we investigate a class of non-monotone reaction-diffusion
equations with distributed delay and a homogenous boundary Neumann condition,
which have a positive steady state. The main concern is the global attractivity
of the unique positive steady state. To achieve this, we use an argument of a
sub and super-solution combined with fluctuation method. We also give a
condition for which the exponential stability of the positive steady state is
reached. As an example, we apply our results to diffusive Nicholson blowflies
and diffusive Mackey-Glass equation with distributed delay. We point out that
we obtain some new results on exponential stability of the positive steady
state for these cited models.
