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In this study, we aim to discuss the question of the existence and periodicity of solutions of nonautonomous functional differential equations with infinite delay in the framework of phase spaces \(\mathscr {B}\) which is defined axiomatically. Our approach relies on Sadovskii’s fixed-point theorem, assuming the family of linear operators A(t) to be nondensely defined while satisfying the Acquistapace–Terreni conditions. Finally, we present an application to exemplify and demonstrate the outcomes of our findings.

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The Periodicity of Solutions of Nonautonomous Functional Differential Equations with Infinite Delay via Sadovskii’s Fixed-Point Theorem

  • 会议论文

  • 发表日期：

    2025年

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  • Ismail Oumadane,
  • Hanaa Zitane

摘要

In this study, we aim to discuss the question of the existence and periodicity of solutions of nonautonomous functional differential equations with infinite delay in the framework of phase spaces \(\mathscr {B}\) which is defined axiomatically. Our approach relies on Sadovskii’s fixed-point theorem, assuming the family of linear operators A(t) to be nondensely defined while satisfying the Acquistapace–Terreni conditions. Finally, we present an application to exemplify and demonstrate the outcomes of our findings.