Academic Editor: Youssef EL FOUTAYENI
Received |
Accepted |
Published |
21 January 2020 |
05 February 2020 |
10 March 2020 |
Abstract: In this work, we study the existence of periodic solutions for a class of linear partial functional differential equations with infinite delay. We assume that the linear part is not necessarily densely defined and satisfies the known Hille-Yosida condition. The perturbation theory of semi-Fredholm operators is using to show that the Poincar\'{e} map satisfies all conditions of the Chow and Hale fixed point theorem, which allows us to prove the existence of periodic solutions. In addition we present a sufficient condition to guarantee the uniqueness of such solution and an example is also given to illustrate our results.
