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Global Solutions for Nonlinear Delay Evolution Inclusions with Nonlocal Initial Conditions
Springer Science and Business Media LLC - - 2012
The Metric Integral of Set-Valued Functions
Springer Science and Business Media LLC - Tập 26 - Trang 867-885 - 2017
This paper introduces a new integral of univariate set-valued functions of bounded variation with compact images in
${\mathbb {R}}^d$
. The new integral, termed the metric integral, is defined using metric linear combinations of sets and is shown ......
Representative Functions, Variational Convergence and Almost Convexity
Springer Science and Business Media LLC - Tập 32 - Trang 1-45 - 2024
We develop a new epi-convergence based on the use of bounded convergent nets on the product topology of the strong topology on the primal space and weak star topology on the dual space of a general real Banach space. We study the propagation of the associated variational convergences through conjugation of convex functions defined on this product space. These results are then applied to the proble......
Morse Decompositions for Nonautonomous General Dynamical Systems
Springer Science and Business Media LLC - Tập 22 - Trang 117-154 - 2013
The Morse decomposition theory for nonautonomous general dynamical systems (set-valued dynamical systems) and differential inclusions is established. The stability of Morse decompositions of pullback attractors is also addressed.
Uniqueness for Quasi-variational Inequalities
Springer Science and Business Media LLC - Tập 24 - Trang 285-297 - 2015
This paper presents a uniqueness result for a quasi-variational inequality QVI(1) that, in contrast to existing results, does not require the projection mapping on a variable closed and convex set to be a contraction. Our basic idea is to find a simple QVI(0), for example a variational inequality, for which we can show the existence of a unique solution. Further, exploiting some nonsingularity con......
A Variational Approach to Perturbation Feedback Control for Optimal Control Problems with Terminal Constraints and Free Terminal Time
Springer Science and Business Media LLC - Tập 27 - Trang 309-330 - 2018
Using the method of characteristics, for an optimal control problem with terminal constraints and free terminal time, we construct a family of extremals along a non-singular reference extremal and analyze when this family defines an embedding, i.e., a local field of extremals. An essential aspect of this construction is the desingularization of the transversality conditions near the terminal point......
Bornological Convergences on the Hyperspace of a Uniformizable Space
Springer Science and Business Media LLC - Tập 24 - Trang 597-618 - 2016
Bornological convergence is a generalization of the well known Attouch–Wets convergence. Our aim is to compare lower, upper and “two-sided” convergences generated by two compatible uniformities and two arbitrary bornologies. Moreover, the comparison of convergences induced by bounded-proximal topologies is characterized.
Computing Proximal Points of Convex Functions with Inexact Subgradients
Springer Science and Business Media LLC - - 2018
Continuity of the Metric Projection and Local Solar Properties of Sets
Springer Science and Business Media LLC - - 2017
The paper is concerned with local approximative and geometric properties of sets, with particular emphasis on strict solarity of such sets under certain constraints on the continuity of metric projections. A partial answer is given to the question due to B. Brosowski and F. Deutsch as to when the class of strict protosuns (Kolmogorov sets) coincides with the class of sets with outer radially conti......
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