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

• 成果类型: Article
• 署名作者: Adly, Samir; Hantoute, Abderrahim; Thera, Michel
• 署名单位: Universite de Limoges; Universidad de Chile; Federation University Australia
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-015-0938-6
• 发表日期: 2016
• 页码: 349-374
• 关键词: stability theory

摘要

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.