Galerkin-Like Method for Integro-Differential Inclusions with Applications to Volterra Sweeping Processes

Pedro Pérez-Aros (), Manuel Torres-Valdebenito () and Emilio Vilches ()
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Pedro Pérez-Aros: Universidad de Chile
Manuel Torres-Valdebenito: Universidad de Chile
Emilio Vilches: Universidad de Chile

Journal of Optimization Theory and Applications, 2025, vol. 205, issue 2, No 9, 30 pages

Abstract: Abstract In this paper, we develop the Galerkin-like method to address first-order integro-differential inclusions. Under compactness or monotonicity conditions, we obtain new results for the existence of solutions for this class of problems, which generalize existing results in the literature and provide new insights for differential inclusions with an unbounded right-hand side. The effectiveness of the proposed approach is illustrated by presenting new existence results for nonconvex state-dependent Volterra sweeping processes, where the right-hand side is unbounded, and the classical theory of differential inclusions is not applicable. This is the first result of its kind. The paper concludes with an application to the existence of an optimal control problem governed by nonconvex state-dependent Volterra sweeping processes in finite dimensions.

Keywords: Integro-differential inclusions; Galerkin-like method; Sweeping process; Subsmooth sets; Normal cone; Measure of non-compactness; 34A60; 49J52; 34G25; 49J53 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02653-0

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