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Author Graef, John R
Title Impulsive Differential Inclusions : A Fixed Point Approach
Imprint Berlin/Boston : De Gruyter, Inc., 2013
©2013
book jacket
Descript 1 online resource (400 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
Series De Gruyter Series in Nonlinear Analysis and Applications Ser. ; v.20
De Gruyter Series in Nonlinear Analysis and Applications Ser
Note Intro -- Notations -- 1 Introduction and Motivations -- 1.1 Introduction -- 1.2 Motivational Models -- 1.2.1 Kruger-Thiemer Model -- 1.2.2 Lotka-Volterra Model -- 1.2.3 Pulse Vaccination Model -- 1.2.4 Management Model -- 1.2.5 Some Examples in Economics and Biomathematics -- 2 Preliminaries -- 2.1 Some Definitions -- 2.2 Some Properties in Fréchet Spaces -- 2.3 Some Properties of Set-valued Maps -- 2.3.1 Hausdorff Metric Topology -- 2.3.2 Vietoris Topology -- 2.3.3 Continuity Concepts and Their Relations -- 2.3.4 Selection Functions and Selection Theorems -- 2.3.5 Hausdorff Continuity -- 2.3.6 Measurable Multifunctions -- 2.3.7 Decomposable Selection -- 2.4 Fixed Point Theorems -- 2.5 Measures of Noncompactness: MNC -- 2.6 Semigroups -- 2.6.1 C0-semigroups -- 2.6.2 Integrated Semigroups -- 2.6.3 Examples -- 2.7 Extrapolation Spaces -- 3 FDEs with Infinite Delay -- 3.1 First Order FDEs -- 3.1.1 Examples of Phase Spaces -- 3.1.2 Existence and Uniqueness on Compact Intervals -- 3.1.3 An Example -- 3.2 FDEs with Multiple Delays -- 3.2.1 Existence and Uniqueness Result on a Compact Interval -- 3.2.2 Global Existence and Uniqueness Result -- 3.3 Stability -- 3.3.1 Stability Result -- 3.4 Second Order Impulsive FDEs -- 3.4.1 Existence and Uniqueness Results -- 3.5 Global Existence and Uniqueness Result -- 3.5.1 Uniqueness Result -- 3.5.2 Example -- 3.5.3 Stability -- 4 Boundary Value Problems on Infinite Intervals -- 4.1 Introduction -- 4.1.1 Existence Result -- 4.1.2 Uniqueness Result -- 4.1.3 Example -- 5 Differential Inclusions -- 5.1 Introduction -- 5.1.1 Filippov's Theorem -- 5.1.2 Relaxation Theorem -- 5.2 Functional Differential Inclusions -- 5.2.1 Filippov's Theorem for FDIs -- 5.2.2 Some Properties of Solution Sets -- 5.3 Upper Semicontinuity without Convexity -- 5.3.1 Nonconvex Theorem and Upper Semicontinuity -- 5.3.2 An Application
5.4 Inclusions with Dissipative Right Hand Side -- 5.4.1 Existence and Uniqueness Result -- 5.5 Directionally Continuous Selection and IDIs -- 5.5.1 Directional Continuity -- 6 Differential Inclusions with Infinite Delay -- 6.1 Existence Results -- 6.2 Boundary Differential Inclusions -- 7 Impulsive FDEs with Variable Times -- 7.1 Introduction -- 7.1.1 Existence Results -- 7.1.2 Neutral Functional Differential Equations -- 7.2 Impulsive Hyperbolic Differential Inclusions with Infinite Delay -- 7.3 Existence Results -- 7.3.1 Phase Spaces -- 7.3.2 The Nonconvex Case -- 8 Neutral Differential Inclusions -- 8.1 Filippov's Theorem -- 8.2 The Relaxed Problem -- 8.2.1 Existence and Compactness Result: an MNC Approach -- 9 Topology and Geometry of Solution Sets -- 9.1 Background in Geometric Topology -- 9.2 Aronszajn Type Results -- 9.2.1 Solution Sets for Impulsive Differential Equations -- 9.3 Solution Sets of Differential Inclusions -- 9.4 σ-selectionable Multivalued Maps -- 9.4.1 Contractible and Rδ -contractible -- 9.4.2 Rδ-sets -- 9.5 Impulsive DIs on Proximate Retracts -- 9.5.1 Viable Solution -- 9.6 Periodic Problems -- 9.6.1 Poincaré Translation Operator -- 9.6.2 Existence Result -- 9.7 Solution Set for Nonconvex Case -- 9.7.1 Continuous Selection and AR of Solution Sets -- 9.8 The Terminal Problem -- 9.8.1 Existence and Solution Set -- 10 Impulsive Semilinear Differential Inclusions -- 10.1 Nondensely Defined Operators -- 10.2 Integral Solutions -- 10.3 Exact Controllability -- 10.3.1 Controllability of Impulsive FDIs -- 10.3.2 Controllability of Impulsive Neutral FDIs -- 10.4 Controllability in Extrapolation Spaces -- 10.5 Second Order Impulsive Semilinear FDIs -- 10.5.1 Mild Solutions -- 10.5.2 Filippov's Theorem -- 10.5.3 Filippov-Wazewski's Theorem -- 11 Selected Topics -- 11.1 Stochastic Differential Equations -- 11.1.1 Itô Integral
11.1.2 Definition of a Mild Solution -- 11.1.3 Existence and Uniqueness -- 11.1.4 Global Existence and Uniqueness -- 11.2 Impulsive Sweeping Processes -- 11.2.1 Preliminaries in Nonsmooth Analysis -- 11.2.2 Uniqueness Result -- 11.3 Integral Inclusions of Volterra Type in Banach Spaces -- 11.3.1 Resolvent Family -- 11.3.2 Existence results -- 11.3.3 The Convex Case: an MNC Approach -- 11.3.4 The Nonconvex Case -- 11.4 Filippov's Theorem -- 11.4.1 Filippov's Theorem on a Bounded Interval -- 11.5 The Relaxed Problem -- Appendix -- A.1 CM ech Homology Functor with Compact Carriers -- A.2 The Bochner Integral -- A.3 Absolutely Continuous Functions -- A.4 Compactness Criteria in C([a,b]), Cb([0, ∞), E), and PC([a,b],E) -- A.5 Weak-compactness in L1 -- A.6 Proper Maps and Vector Fields -- A.7 Fundamental Theorems in Functional Analysis -- Bibliography -- Index
The series is devoted to the publication of high-level monographs which cover the whole spectrum of current nonlinear analysis and applications in various fields, such as optimization, control theory, systems theory, mechanics, engineering, and other sciences. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of nonlinear analysis. Contributions which are on the borderline of nonlinear analysis and related fields and which stimulate further research at the crossroads of these areas are particularly welcome. Please submit book proposals toJürgen Appell
Description based on publisher supplied metadata and other sources
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
Link Print version: Graef, John R. Impulsive Differential Inclusions : A Fixed Point Approach Berlin/Boston : De Gruyter, Inc.,c2013 9783110293616
Subject Boundary value problems.;Differential equations.;Prediction theory.;Stochastic processes
Electronic books
Alt Author Henderson, Johnny
Ouahab, Abdelghani
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