Existence of Asymptotically Periodic Solutions of Partial Functional Differential Equations with State-Dependent Delay

In this paper, we are concerned with systems determined by partial differential equations with infinite and state-dependent delay. To study the system, we model the equation as an abstract retarded functional differential equations with infinite and state-dependent delay. We establish the existence of mild solutions, and the existence of S-asymptotically periodic solutions and asymptotically periodic solutions using local Lipschitz conditions on the involved functions. We apply our results to study the existence of asymptotically periodic solutions of a partial differential equation with infinite and state-dependent delay. © 2019 Informa UK Limited, trading as Taylor & Francis Group.