| Description |
1 online resource (x, 313 pages) |
| Series |
Mathematics in science and engineering ; v. 167 |
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Mathematics in science and engineering ; v. 167.
|
| Contents |
Front Cover; Volterra Integral and Differential Equations; Copyright Page; Contents; Preface; Chapter 0. Introduction and Overview; 0.1. Statement of Purpose; 0.2. An Overview; Chapter 1. The General Problems; 1.1. Introduction; 1.2. Relations between Differential and Integral Equations; 1.3. A Glance at Initial Conditions and Existence; 1.4. Building the Intuition; 1.5. Reducible Equations; Chapter 2. Linear Equations; 2.1. Existence Theory; 2.2. Linear Properties; 2.3. Convolution and the Laplace Transform; 2.4. Stability; 2.5. Liapunov Functionals and Small Kernels |
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2.6. Uniform Asymptotic Stability2.7. Reducible Equations Revisited; 2.8. The Resolvent; Chapter 3. Existence Properties; 3.1. Definitions, Background, and Review; 3.2. Existence and Uniqueness; 3.3. Continuation of Solutions; 3.4. Continuity of Solutions; Chapter 4. History, Examples, and Motivation; 4.0. Introduction; 4.1. Volterra and Mathematical Biology; 4.2. Renewal Theory; 4.3. Examples; Chapter 5. Instability, Stability, and Perturbations; 5.1. The Matrix ATB + BA; 5.2. The Scalar Equation; 5.3. The Vector Equation; 5.4. Complete Instability; Chapter 6. Stability and Boundedness |
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6.1. Stability Theory for Ordinary Differential Equations6.2. Construction of Liapunov Functions; 6.3. A First Integral Liapunov Functional; 6.4. Nonlinear Considerations and an Annulus Argument; 6.5. A Functional in the Unstable Case; Chapter 7. Perturbations; 7.1. A Converse Theorem Yielding a Perturbation Result; 7.2. Boundedness under Perturbations; 7.3. Additive Properties of Functionals; Chapter 8. Functional Differential Equations; 8.0. Introduction; 8.1. Existence and Uniqueness; 8.2. Asymptotic Stability; 8.3. Equations with Bounded Delay; 8.4. Boundedness with Unbounded Delay |
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8.5. Limit Sets8.6. Periodic Solutions; 8.7. Limit Sets and Unbounded Delays; References; Author Index; Subject Index |
| Summary |
Volterra integral and differential equations |
| Bibliography |
Includes bibliographical references (pages 303-307) and indexes |
| Notes |
Print version record |
| Subject |
Volterra equations.
|
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Integro-differential equations.
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MATHEMATICS -- Differential Equations -- General.
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Integro-differential equations
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Volterra equations
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| Form |
Electronic book
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| ISBN |
9780080956732 |
|
0080956734 |
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