On state-dependent sweeping process in Banach spaces (Q1711853)

The authors study existence results for a perturbed first order differential inclusion governed by the proximal normal cone to a moving set depending on the time and on the state in a separable reflexive uniformly smooth Banach space. They derive the existence of Lipschitz solutions for the differential inclusion and the estimation of the derivative of solutions by using the theory of Banach spaces, the methods of nonsmooth analysis and the technique of approximation. There is an open question of the continuity of the mapping \(v\rightarrow P_{C(t,v)}(u)\) in the comments of this paper.