Differential and Integral Inequalities

Name: Differential and Integral Inequalities | Theory and Applications
Brand: Academic Press
Price: 90.95 EUR
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Theory and Applications

Lakshmikantham(Herausgeber*in)

Academic Press

Erschienen am 14. Mai 2014

405 Seiten

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978-0-08-095563-6 (ISBN)

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Front Cover
Differential and Integral Inequalities: Theory and Applications
Copyright Page
Contents
Preface
PART 1: ORDINARY DIFFERENTIAL EQUATIONS
Chapter 1.
1.0. Introduction
1.1. Existence and Continuation of Solutions
1.2. Scalar Differential Inequalities
1.3. Maximal and Minimal Solutions
1.4. Comparison Theorems
1.5. Finite Systems of Differential Inequalities
1.6. Minimax Solutions
1.7. Further Comparison Theorems
1.8. Infinite Systems of Differential Inequalities
1.9. Integral Inequalities Reducible to Differential Inequalities
1.10. Differential Inequalities in the Sense of Caratheodory
1.11. Notes
Chapter 2.
2.0. Introduction
2.1. Global Existence
2.2. Uniqueness
2.3. Convergence of Successive Approximations
2.4. Chaplygin's Method
2.5. Dependence on Initial Conditions and Parameters
2.6. Variation of Constants
2.7. Upper and Lower Bounds
2.8. Componentwise Bounds
2.9. Asymptotic Equilibrium
2.10. Asymptotic Equivalence
2.11. A Topological Principle
2.12. Applications of Topological Principle
2.13. Stability Criteria
2.14. Asymptotic Behavior
2.15 Periodic and Almost Periodic Systems
2.16. Notes
Chapter 3.
3.0. Introduction
3.1. Basic Comparison Theorems
3.2. Definitions
3.3. Stability
3.4. Asymptotic Stability
3.5. Stability of Perturbed Systems
3.6. Converse Theorems
3.7. Stability by the First Approximation
3.8. Total Stability
3.9. Integral Stability
3.10. L"-Stability
3.11. Partial Stability
3.12. Stability of Differential Inequalities
3.13. Boundcdness and Lagrange Stability
3.14. Eventual Stability
3.15. Asymptotic Behavior
3.16. Relative Stability
3.17. Stability with Respect to a Manifold
3.18. Almost Periodic Systems
3.19. Uniqueness and Estimates
3.20. Continuous Dependence and the Method of Averaging
3.21. Notes
Chapter 4.
4.0. Introduction
4.1. Main Comparison Theorem
4.2. Asymptotic Stability
4.3. Instability
4.4. Conditional Stability and Boundedness
4.5. Converse Theorems
4.6. Stability in Tube-like Domain
4.7. Stability of Asymptotically Self-Invariant Sets
4.8. Stability of Conditionally Invariant Sets
4.9. Existence and Stability of Stationary Points
4.10. Notes
PART 2: VOLTERRA INTEGRAL EQUATIONS
Chapter 5.
5.0. Introduction
5.1. Integral Inequalities
5.2. Local and Global Existence
5.3. Comparison Theorems
5.4. Approximate Solutions, Bounds, and Uniqueness
5.5. Asymptotic Behavior
5.6. Perturbed Integral Equations
5.7. Admissibility and Asymptotic Behavior
5.8. Integrodifferential Inequalities
5.9. Notes
Bibliography
Author Index
Subject Index

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