Eberlein-Weakly Almost Periodic Solutions for Some Partial Functional Differential Equation with Infinite Delay

• El Hadi Ait Dads ^[1] ; Brahim Es-sebbar ^[2] ; Samir Fatajou ^[2] ; Zakaria Zizi ^[2]
  1. [1] Université Cadi Ayyad & Sorbonne Université
  2. [2] Université Cadi Ayyad
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 3, 2024
• Idioma: inglés
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• Resumen

  • 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.