Existence of solutions for a class of implicit differential inclusions: a constructive proof (Q1086403)

The author shows that \(x(t)\in M^{-1}(-C(x(t)))\) a.e., \(x(0)=x_ 0\) (M: \({\mathbb{R}}^ n\to 2^{{\mathbb{R}}^ n}\), \(C: {\mathbb{R}}^ n\to 2^{{\mathbb{R}}^ n})\) admits solutions which can be approximated by some kind of Euler approximation if M is maximal monotone, if the range of M contains the range of -C, and if C coincides on a neighbourhood D of \(x_ 0\) with the sum \(g+\partial \phi -\partial \psi\) of a continuous function g and the difference of the subdifferentials of two convex functions \(\phi\) and \(\psi\), which are finite on D.