Resolving implicit nonconvex state-dependent sweeping processes in Banach spaces

Abstract

We study a nonconvex implicit sweeping process in which the moving constraint set depends on both time and the state variable. The analysis is carried out in a 2-uniformly convex and smooth Banach space via a generalized projection approach based on a duality mapping. By transforming the differential inclusion into an explicit evolution equation and imposing a suitable growth condition, we establish the existence of Lipschitz solutions. Several examples are provided to illustrate the applicability of the main results.