Existence Results for State-Dependent Maximal Monotone Differential Inclusions: Fixed Point Approach

Abstract

In this article, we give a new proof of the existence of absolutely continuous solutions for a class of first-order state-dependent maximal monotone differential inclusions. The existence result is obtained by using Schauder’s fixed point theorem. In addition, a stability result is provided. Finally, using a suitable reduction of order technique, we give a new existence result for a general second-order state-dependent maximal monotone differential inclusion.