Nonlinear Delay Evolution Inclusions on Graphs

International audienceWe prove a necessary and a sufficient condition for a time-dependent closed set to be viable with respect to a delay evolution inclusion. An application to a null controllability problem is also included

Nonsmooth Lyapunov pairs for differential inclusions governed by operators with nonempty interior domain

The general theory of Lyapunov stability of first-order differential inclusions in Hilbert spaces has been studied by the authors in the previous paper (Adly et al. in Nonlinear Anal 75(3): 985–1008, 2012). This new contribution focuses on the case when the interior of the domain of the maximally monotone operator governing the given differential inclusion is nonempty; this includes in a natural way the finite-dimensional case. The current setting leads to simplified, more explicit criteria and permits some flexibility in the choice of the generalized subdifferentials. Some consequences of the viability of closed sets are given. Our analysis makes use of standard tools from convex and variational analysis. © 2015, Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society