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

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 operato...

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Bibliographic Details
Published in:Nonlinear analysis Vol. 75; no. 3; pp. 985 - 1008
Main Authors: Adly, S., Hantoute, A., Théra, M.
Format: Journal Article
Language:English
Published: Amsterdam Elsevier Ltd 01.02.2012
Elsevier
Subjects:
Contingent derivatives
Criteria
Derivatives
Differential inclusions
Differentiation
Exact sciences and technology
Global analysis, analysis on manifolds
Hilbert space
Inclusions
Invariance of sets
Lipschitz perturbations
Lower semicontinuous Lyapunov pairs and functions
Mathematical analysis
Mathematics
Maximal monotone operators
Nonlinearity
Operators
Optimization and Control
Ordinary differential equations
Perturbation methods
Sciences and techniques of general use
Subdifferential sets
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Differential inclusions
Maximal monotone operators
Invariance of sets
Contingent derivatives
Lower semicontinuous Lyapunov pairs and functions
Subdifferential sets
Lipschitz perturbations
Lower semicontinuous Lyapunov pairs and
functions
Nonlinear analysis
Differential inclusion
Mathematical model
ISSN:0362-546X, 1873-5215
Online Access:Get full text
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Summary: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.
Bibliography:ObjectType-Article-2
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ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2010.11.009