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

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Abstract

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.

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Acknowledgements

The authors would like to express their thanks to the editor and the anonymous referees for the careful reading of the manuscript and for their suggestions and comments that improved the quality of the paper.

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Authors and Affiliations

  1. Département de Mathématiques, Faculté des Sciences Semlalia, Université Cadi Ayyad, B.P. 2390, Marrakesh, Morocco

    El Hadi Ait Dads

  2. UMMISCO UMI 209 IRD Bondy, Sorbonne Université, Paris, France

    El Hadi Ait Dads

  3. Département de Mathématiques, Faculté des Sciences et Techniques Guéliz, Laboratoire de Mathématiques Appliquées et Informatique, Université Cadi Ayyad, B.P. 549, Marrakesh, Morocco

    Brahim Es-sebbar

  4. Directeur de l’Ecole Supérieure de Technologie d’El Kelaa des Sraghna, Université Cadi Ayyad, B.P. 104, El Kelaa des Sraghna, Morocco

    Samir Fatajou

  5. Laboratoire L. M. D. P., Faculté des Sciences Semlalia, Université Cadi Ayyad, P.O. Box 2390, Marrakesh, Morocco

    Zakaria Zizi

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  1. El Hadi Ait Dads
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  2. Brahim Es-sebbar
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  3. Samir Fatajou
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  4. Zakaria Zizi
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Correspondence to Zakaria Zizi.

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Ait Dads, E.H., Es-sebbar, B., Fatajou, S. et al. Eberlein-Weakly Almost Periodic Solutions for Some Partial Functional Differential Equation with Infinite Delay. Qual. Theory Dyn. Syst. 23, 125 (2024). https://doi.org/10.1007/s12346-024-00977-2

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