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On the almost periodic and almost automorphic solution for linear renewal equations with infinite delay via reduction principle

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  • Afoukal, Abdallah
  • El Attaouy, Meryem
  • Ezzinbi, Khalil

Abstract

We prove, for nonhomogeneous autonomous linear renewal equations with infinite delay, that if the forcing term is almost periodic (respectively, almost automorphic), then every bounded solution on the whole real line is also almost periodic (respectively, almost automorphic). Additionally, the existence of a bounded solution on the half-positive real line implies the existence of an almost periodic (respectively, almost automorphic) solution. Next, we present a result on uniqueness. To illustrate our results, we propose an application to an epidemic model with waning immunity.

Suggested Citation

  • Afoukal, Abdallah & El Attaouy, Meryem & Ezzinbi, Khalil, 2024. "On the almost periodic and almost automorphic solution for linear renewal equations with infinite delay via reduction principle," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    • Handle: RePEc:eee:chsofr:v:181:y:2024:i:c:s0960077924001607
    DOI: 10.1016/j.chaos.2024.114609
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    References listed on IDEAS

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    1. Gyllenberg, Mats & Scarabel, Francesca & Vermiglio, Rossana, 2018. "Equations with infinite delay: Numerical bifurcation analysis via pseudospectral discretization," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 490-505.
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