Nonsmooth Lyapunov pairs for differential inclusions governed by operators with nonempty interior domain
Résumé
The general theory of Lyapunov stability of first-order differential inclu- sions 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 con- sequences of the viability of closed sets are given. Our analysis makes use of standard tools from convex and variational analysis.
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