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.