Article Dans Une Revue Nonlinear Analysis: Theory, Methods and Applications Année : 2012

Nonsmooth Lyapunov pairs for infinite-dimensional first-order differential inclusions

Samir Adly
Abdelrrahim Hantoute
  • Fonction : Auteur
Michel Théra

Résumé

The main objective of this paper is to provide new explicit criteria to characterize weak lower semicontinuous Lyapunov pairs or functions associated to first-order differential inclusions in Hilbert spaces. These inclusions are governed by a Lipschitzian perturbation of a maximally monotone operator. The dual criteria we give are expressed by means of the proximal and basic subdifferentials of the nominal functions while primal conditions are described in terms of the contingent directional derivative. We also propose a unifying review of many other criteria given in the literature. Our approach is based on advanced tools of variational analysis and generalized differentiation.

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hal-00586942 , version 1 (03-04-2019)

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Samir Adly, Abdelrrahim Hantoute, Michel Théra. Nonsmooth Lyapunov pairs for infinite-dimensional first-order differential inclusions. Nonlinear Analysis: Theory, Methods and Applications, 2012, 75 (3), pp.985-1008. ⟨10.1016/j.na.2010.11.009⟩. ⟨hal-00586942⟩
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