Ultimate boundedness and periodicity for some partial functional differential equations with infinite delay

In this work we study the existence of periodic solutions for some partial functional differential equation with infinite delay. We assume that the linear part is not necessarily densely defined and satisfies the known Hille–Yosida condition. Firstly, we give some estimates of the solutions. Secondly, we prove that the Poincaré map is condensing which allows us to prove the existence of periodic solutions when the solutions are ultimately bounded.