Resumen de Eberlein-Weakly Almost Periodic Solutions for Some Partial Functional Differential Equation with Infinite Delay
El Hadi Ait Dads, Brahim Es-sebbar, Samir Fatajou, Zakaria Zizi
In this work, we prove some new results concerning the class of Eberlein weakly almost periodic functions in Stepanov’s sense. We prove that if the forcing term of a partial functional differential equation with infinite delay is Eberlein-weakly almost periodic in Stepanov’s sense, then the solution is even Eberlein-weakly almost periodic. This shows that a less regular almost periodic behavior in the forcing term yields a more regular almost periodic behavior in the solution. The theoretical results are illustrated in the Lotka–Volterra model.
