  In the present paper, we investigate both the global exponential stability
and the existence of a periodic solution of a general differential equation
with unbounded distributed delays. The main stability criterion depends on the
dominance of the non-delay terms over the delay terms. The criterion for the
existence of a periodic solution is obtained with the application of the
coincide degree theorem. We use the main results to get criteria for the
existence and global exponential stability of periodic solutions of a
generalized higher-order periodic Cohen-Grossberg neural network model with
discrete-time varying delays and infinite distributed delays. Additionally, we
provide a comparison with the results in the literature and a numerical
simulation to illustrate the effectiveness of some of our results.
