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<p>In this paper, we establish several sufficient conditions ensuring the existence and uniqueness of the solution for a novel type of set differential equations with non-instantaneous impulses (NISDEs), leveraging the principle of contraction mapping and Leray-Schauder fixed point theorem. Furthermore, we delve into the concepts of Ulam-type stability for this class of equations, and primarily present the essential sufficient conditions for ensuring Ulam-Hyers-Rassias stability (UHRs). Finally, we provide an example to demonstrate the main findings of our study.</p>

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Ulam-type stability of set differential equations with non-instantaneous impulses

  • 期刊论文

  • 发表日期：

    2026年1月8日

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  • Dan Yang,
  • Mengmeng Li

摘要

In this paper, we establish several sufficient conditions ensuring the existence and uniqueness of the solution for a novel type of set differential equations with non-instantaneous impulses (NISDEs), leveraging the principle of contraction mapping and Leray-Schauder fixed point theorem. Furthermore, we delve into the concepts of Ulam-type stability for this class of equations, and primarily present the essential sufficient conditions for ensuring Ulam-Hyers-Rassias stability (UHRs). Finally, we provide an example to demonstrate the main findings of our study.