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

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• 作者：Samir Adly ; Abderrahim Hantoute ; Michel Théra
• 刊名：Mathematical Programming
• 出版年：2016
• 出版时间：June 2016
• 年：2016
• 卷：157
• 期：2
• 页码：349-374
• 全文大小：531 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Calculus of Variations and Optimal Control
  Mathematics of Computing
  Numerical Analysis
  Combinatorics
  Mathematical and Computational Physics
  Mathematical Methods in Physics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1436-4646
• 卷排序：157

文摘

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.KeywordsEvolution differential inclusionsMaximally monotone operatorsLower semicontinuous Lyapunov pairs and functions Invariant setsGeneralized subdifferentials