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

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