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Unique Solvability of Infinite Dimensional Differential Sweeping Systems

Author

Listed:
  • Jinsheng Du

    (Guangxi University)

  • Stanisław Migórski

    (Jagiellonian University in Krakow)

  • Emilio Vilches

    (Universidad de O’Higgins)

  • Shengda Zeng

    (Chongqing Normal University)

Abstract

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.

Suggested Citation

  • Jinsheng Du & Stanisław Migórski & Emilio Vilches & Shengda Zeng, 2026. "Unique Solvability of Infinite Dimensional Differential Sweeping Systems," Journal of Optimization Theory and Applications, Springer, vol. 208(1), pages 1-37, January.
    • Handle: RePEc:spr:joptap:v:208:y:2026:i:1:d:10.1007_s10957-025-02837-8
    DOI: 10.1007/s10957-025-02837-8
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