| Description |
1 online resource (ix, 390 pages). |
| Physical Medium |
polychrome |
| Description |
text file |
| Series |
Mathematics in science and engineering ; v. 55
|
|
Mathematics in science and engineering ; v. 55.
|
| Bibliography |
Includes bibliographical references (pages 355-384) and indexes. |
| 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. |
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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. |
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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. |
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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. |
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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. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Inequalities (Mathematics)
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Inequalities (Mathematics) |
| Genre/Form |
Electronic books.
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| Added Author |
Lakshmikantham, V., 1926-2012.
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Leela, S.
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| Added Title |
Ordinary differential equations |
| Other Form: |
Print version: Differential and integral inequalities. New York : Academic Press, 1969 9780124341012 (OCoLC)181657079 |
| ISBN |
9780080955636 (electronic book) |
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0080955630 (electronic book) |
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