Existence of asymptotically periodic solutions of partial functional differential equations with state-dependent delay. Issue 14 (26th October 2021) - Andrade, Filipe; Cuevas, Claudio; Henríquez, Hernán R.
ABSTRACT: 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.