Existence of solutions to the state dependent sweeping process with delay

Abstract

In this paper, we prove, via new projection algorithm, the existence of solutions for functional differential inclusion governed by state dependent sweeping process with perturbation depending on all variables and with delay.

Robust output convergence of heterogeneous networks via nonsmooth hard-threshold couplings

“…This section presents the proof of Theorem 6 regarding existence of absolutely continuous solutions of the differential inclusion (13). The proof is an adaptation and an extension of the proof in [25] and is presented here for completeness. The proof is divided in several subsections.…”