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Bulletin of the Malaysian Mathematical Sciences Society, 2022 AbstractIn this paper, Sobolev-type conformable fractional stochastic evolution inclusions with Clarke subdifferential and nonlocal conditions are studied. By using fractional calculus, stochastic analysis, properties of Clarke subdifferential and nonsmooth analysis, sufficient conditions for nonlocal controllability for the considered problem are ...
Maria Alessandra Ragusa
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Separation of convex sets by Clarke subdifferential
Optimization, 2010In this article we consider a separation technique proposed in J. Grzybowski, D. Pallaschke, and R. Urbanski (A pre-classification and the separation law for closed bounded convex sets, Optim. Method Softw. 20(2005), pp. 219–229) for separating two convex sets A and B with another convex set C. We prove that in a finite dimension C can be chosen as the
GAUDIOSO, MANLIO +2 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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Approximate controllability for stochastic evolution inclusions of Clarke’s subdifferential type
Applied Mathematics and Computation, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Liang Lu, Zhenhai Liu, Maojun Bin
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Clarke subdifferential for lipschitzian multivalued mappings
Cybernetics and Systems Analysis, 1992zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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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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Existence and controllability for fractional evolution inclusions of Clarke’s subdifferential type
Applied Mathematics and Computation, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Liu, Zhenhai, Zeng, Biao
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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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The Clarke and Michel-Penot Subdifferentials of the Eigenvalues of a Symmetric Matrix
Computational Optimization and Applications, 1999zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hiriart-Urruty, J.-B., Lewis, A. S.
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