Impulsive Differential Inclusions A Fixed Point Approach.
Title:
Impulsive Differential Inclusions A Fixed Point Approach.
Author:
Ouahab, Abdelghani.
ISBN:
9783110295313
Personal Author:
Publication Information:
Berlin : De Gruyter, 2013.
Physical Description:
1 online resource (412 p.)
Series:
De Gruyter Series in Nonlinear Analysis and Applications
De Gruyter series in nonlinear analysis and applications.
General Note:
Description based upon print version of record.
9.7.1 Continuous Selection and AR of Solution Sets
Contents:
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 Selection2.4 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 Results3.5 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 Side5.4.1 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
Abstract:
Impulsive differential equations have been developed in modeling impulsive problems in physics, population dynamics, ecology, biotechnology, industrial robotics, pharmacokinetics, optimal control, etc. The questions of existence and stability of solutions for different classes of initial values problems for impulsive differential equations and inclusions with fixed and variable moments are considered in detail. Attention is also given to boundary value problems and relative questions concerning differential equations. This monograph addresses a variety of side issues that arise from its simple.
Genre:
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