Unique Solvability of Infinite Dimensional Differential Sweeping Systems

Jinsheng Du (), Stanisław Migórski (), Emilio Vilches () and Shengda Zeng ()
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Jinsheng Du: Guangxi University
Stanisław Migórski: Jagiellonian University in Krakow
Emilio Vilches: Universidad de O’Higgins
Shengda Zeng: Chongqing Normal University

Journal of Optimization Theory and Applications, 2026, vol. 208, issue 1, No 8, 37 pages

Abstract: 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.

Keywords: Differential sweeping process; History-dependent operator; $$\rho $$ ρ -prox-regular set; Measure of noncompactness; Fixed-point; 35M86; 35R70; 47H08; 47J20; 49J53 (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/s10957-025-02837-8

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