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

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• 作者：S.  ; Adly^a ;   ; ^{samir.adly@unilim.fr} ; A.  ; Hantoute^b ;   ; ^{ahantoute@dim.uchile.cl} ; M.  ; Thé ; ra^a ;   ; ¹ ;   ; ^{michel.thera@unilim.fr}
• 关键词：Differential inclusions ; Maximal monotone operators ; Lipschitz perturbations ; Lower semicontinuous Lyapunov pairs and functions ; Invariance of sets ; Subdifferential sets ; Contingent derivatives
• 刊名：Nonlinear Analysis
• 出版年：2012
• 出版时间：February 2012
• 年：2012
• 卷：75
• 期：3
• 页码：985-1008
• 全文大小：380 K

文摘

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.