Differential and integral inequalities :: theory and applications. Volume I, Ordinary differential equations /
Differential and integral inequalities; theory and applications PART A: Ordinary differential equations.
Gespeichert in:
| Weitere Verfasser: | , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York :
Academic Press,
1969.
|
| Schriftenreihe: | Mathematics in science and engineering ;
v. 55. |
| Schlagworte: | |
| Online-Zugang: | Volltext Volltext Volltext |
| Zusammenfassung: | Differential and integral inequalities; theory and applications PART A: Ordinary differential equations. |
| Beschreibung: | 1 online resource (ix, 390 pages) |
| Bibliographie: | Includes bibliographical references (pages 355-384) and indexes. |
| ISBN: | 9780080955636 0080955630 |
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| 505 | 0 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 520 | |a Differential and integral inequalities; theory and applications PART A: Ordinary differential equations. | ||
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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. 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. |
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| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:16:48Z |
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| series | Mathematics in science and engineering ; |
| series2 | Mathematics in science and engineering ; |
| spelling | Differential and integral inequalities : theory and applications. Volume I, Ordinary differential equations / edited by V. Lakshmikantham and S. Leela. Ordinary differential equations New York : Academic Press, 1969. 1 online resource (ix, 390 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier data file Mathematics in science and engineering ; v. 55 Includes bibliographical references (pages 355-384) and indexes. Print version record. 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. 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. Differential and integral inequalities; theory and applications PART A: Ordinary differential equations. Inequalities (Mathematics) http://id.loc.gov/authorities/subjects/sh85065985 Inégalités (Mathématiques) MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Inequalities (Mathematics) fast Lakshmikantham, V., 1926-2012. https://id.oclc.org/worldcat/entity/E39PBJh4xDkWxv4CWJ6trPKWXd Leela, S. http://id.loc.gov/authorities/names/n82032762 has work: Ordinary differential equations Differential and integral inequalities Volume I (Text) https://id.oclc.org/worldcat/entity/E39PCGVCXqFmT67Gc9bGJp9BCP https://id.oclc.org/worldcat/ontology/hasWork Print version: Differential and integral inequalities. New York : Academic Press, 1969 9780124341012 (OCoLC)181657079 Mathematics in science and engineering ; v. 55. http://id.loc.gov/authorities/names/n42015986 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=2268734 Volltext FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=297110 Volltext FWS01 ZDB-4-EBA FWS_PDA_EBA https://www.sciencedirect.com/science/bookseries/00765392/55/part/P1 Volltext |
| spellingShingle | Differential and integral inequalities : theory and applications. Mathematics in science and engineering ; 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. 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. Inequalities (Mathematics) http://id.loc.gov/authorities/subjects/sh85065985 Inégalités (Mathématiques) MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Inequalities (Mathematics) fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85065985 |
| title | Differential and integral inequalities : theory and applications. |
| title_alt | Ordinary differential equations |
| title_auth | Differential and integral inequalities : theory and applications. |
| title_exact_search | Differential and integral inequalities : theory and applications. |
| title_full | Differential and integral inequalities : theory and applications. Volume I, Ordinary differential equations / edited by V. Lakshmikantham and S. Leela. |
| title_fullStr | Differential and integral inequalities : theory and applications. Volume I, Ordinary differential equations / edited by V. Lakshmikantham and S. Leela. |
| title_full_unstemmed | Differential and integral inequalities : theory and applications. Volume I, Ordinary differential equations / edited by V. Lakshmikantham and S. Leela. |
| title_short | Differential and integral inequalities : |
| title_sort | differential and integral inequalities theory and applications ordinary differential equations |
| title_sub | theory and applications. |
| topic | Inequalities (Mathematics) http://id.loc.gov/authorities/subjects/sh85065985 Inégalités (Mathématiques) MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Inequalities (Mathematics) fast |
| topic_facet | Inequalities (Mathematics) Inégalités (Mathématiques) MATHEMATICS Calculus. MATHEMATICS Mathematical Analysis. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=2268734 https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=297110 https://www.sciencedirect.com/science/bookseries/00765392/55/part/P1 |
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