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<p>We study the existence and uniqueness of solutions to a differential sweeping system. This system is an implicit coupled dynamical system consisting of a nonlinear differential equation and a history/state-dependent sweeping process. First, an existence result to a perturbed state-dependent sweeping process is proved based on Schauder’s fixed-point theorem. Next, the unique solvability of a history/state-dependent sweeping process is established by employing a fixed-point theorem for a history-dependent operator. Finally, using tools from nonsmooth analysis and Banach’s fixed-point theorem, we establish the existence and uniqueness of solutions to a differential sweeping system.</p>

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Unique Solvability of Infinite Dimensional Differential Sweeping Systems

  • 期刊论文

  • 发表日期：

    2025年9月9日

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  • Jinsheng Du,
  • Stanisław Migórski,
  • Emilio Vilches,
  • Shengda Zeng

摘要

We study the existence and uniqueness of solutions to a differential sweeping system. This system is an implicit coupled dynamical system consisting of a nonlinear differential equation and a history/state-dependent sweeping process. First, an existence result to a perturbed state-dependent sweeping process is proved based on Schauder’s fixed-point theorem. Next, the unique solvability of a history/state-dependent sweeping process is established by employing a fixed-point theorem for a history-dependent operator. Finally, using tools from nonsmooth analysis and Banach’s fixed-point theorem, we establish the existence and uniqueness of solutions to a differential sweeping system.