New properties of the DD-operator and its applications on the problem of periodic solutions to neutral functional differential system

In this paper, the authors first investigate some new properties of the DD-operator which is associated with neutral functional differential equations. Then, by using these new properties, the problem of existence of periodic solutions of the DD-operator neutral functional differential system is studied. The interesting thing is that the DD-operator is allowed to be unstable, which is generalized by the corresponding studies in the past under the crucial assumption that the DD-operator is stable.