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Article Dans Une Revue Mathematical Programming Année : 2015

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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Dates et versions

hal-01313160 , version 1 (16-07-2018)

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Samir Adly, Abderrahim Hantoute, Michel Théra. Nonsmooth Lyapunov pairs for differential inclusions governed by operators with nonempty interior domain. Mathematical Programming, 2015, pp.1-26. ⟨10.1007/s10107-015-0938-6⟩. ⟨hal-01313160⟩
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