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Differential and integral inequalities : theory and applications. Volume I, Ordinary differential equations / edited by V. Lakshmikantham and S. Leela

Additional Titles:
Ordinary differential equations
Published:
New York : Academic Press, 1969.
Physical Description:
1 online resource (ix, 390 pages).
Additional Creators:
Lakshmikantham, V., 1926- and Leela, S.
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Contents:
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 Caratheodory1.11. 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 Averaging3.21. 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., and 5.4. Approximate Solutions, Bounds, and Uniqueness5.5. 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.
Summary:
Differential and integral inequalities; theory and applications PART A: Ordinary differential equations.
Subject(s):
ISBN:
9780080955636 (electronic bk.)
0080955630 (electronic bk.)
Bibliography Note:
Includes bibliographical references (pages 355-384) and indexes.
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