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A Note On The Clarke Subdifferential
The American Mathematical Monthly, 1998L yON y?N j for every x E U and every Lebesgue null set N containing the set of points where h is not differentiable. By h'(y) we mean the derivative of h at y provided it exists. There are numerous general results about characterizing the Clarke subdifferential. We refer to [2] and [3], from which the following result may be deduced.
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Journal of Nonlinear and Variational Analysis, 2022
Summary: The goal of this paper is to study optimal feedback control for a class of non-autonomous second-order evolution inclusions with Clarke's subdifferential in a separable reflexive Banach space. We only assume that the second order evolution operator involved satisfies the strong continuity condition instead of the compactness, which was used in
Chen, Jun +3 more
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Summary: The goal of this paper is to study optimal feedback control for a class of non-autonomous second-order evolution inclusions with Clarke's subdifferential in a separable reflexive Banach space. We only assume that the second order evolution operator involved satisfies the strong continuity condition instead of the compactness, which was used in
Chen, Jun +3 more
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Neutral fractional stochastic partial differential equations with Clarke subdifferential
Applicable Analysis, 2020By using fractional calculus, stochastic analysis theory and fixed point theorems, sufficient conditions for approximate controllability of nonlocal Sobolev-type neutral fractional stochastic diffe...
Hamdy M. Ahmed +2 more
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Rotund norms, Clarke subdifferentials and extensions of Lipschitz functions
Nonlinear Analysis: Theory, Methods & Applications, 2002It is well known that the Clarke subdifferential of a Lipschitz function is an essential tool in nonsmooth analysis and especially in nonsmooth optimization. Nevertheless, there exists a large class of pathological Lipschitz functions for which this notion provides no information about the local behavior of the function. So in recent papers it is shown
Borwein, Jon +2 more
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2021
In this paper, a class of nonlocal fractional evolution inclusions of Clarke’s subdifferential on semi-infinite intervals is concerned. Based on the semigroup theory, nonlinear alternative of Leray-Schauder and the method of diagonalization process, the nonlocal controllability result is proved. An example is presented to illustrate the main result.
Xuemei Li, Xinge Liu, Meilan Tang
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In this paper, a class of nonlocal fractional evolution inclusions of Clarke’s subdifferential on semi-infinite intervals is concerned. Based on the semigroup theory, nonlinear alternative of Leray-Schauder and the method of diagonalization process, the nonlocal controllability result is proved. An example is presented to illustrate the main result.
Xuemei Li, Xinge Liu, Meilan Tang
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Nonlinear Analysis: Theory, Methods & Applications, 2012
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Integral of the Clarke subdifferential mapping and a generalized Newton–Leibniz formula
Nonlinear Analysis: Theory, Methods & Applications, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Mathematical Methods in the Applied Sciences, 2016
This article investigates the solvability and optimal controls of systems monitored by fractional delay evolution inclusions with Clarke subdifferential type. By applying a fixed‐point theorem of condensing multivalued maps and some properties of Clarke subdifferential, an existence theorem concerned with the mild solution for the system is proved ...
Jiang, Yi-Rong, Huang, Nan-Jing
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This article investigates the solvability and optimal controls of systems monitored by fractional delay evolution inclusions with Clarke subdifferential type. By applying a fixed‐point theorem of condensing multivalued maps and some properties of Clarke subdifferential, an existence theorem concerned with the mild solution for the system is proved ...
Jiang, Yi-Rong, Huang, Nan-Jing
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Journal of Computational and Applied Mathematics, 2018
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Aicha Harrat +2 more
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Aicha Harrat +2 more
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Optimal Control of Fractional Non-Autonomous Evolution Inclusions With Clarke Subdifferential
Fractional Calculus and Applied AnalysisXinge Liu, Xuemei Li
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