Differential Equations in Abstract Spaces
Erschienen am 14. Mai 2014
231 Seiten
978-0-08-095594-0 (ISBN)
Beschreibung
Differential Equations in Abstract Spaces
Weitere Details
Weitere Ausgaben
Andere Ausgaben
Gerasimos E. Ladas | V. Lakshmikantham
Differential Equations in Abstract Spaces
Buch
01/1972
Academic Press
71,61 €
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Inhalt
- Front Cover
- Differential Equations in Abstract Spaces
- Copyright Page
- Contents
- Preface
- Acknowledgments
- Chapter 1. The Calculus of Abstract Functions
- 1.0 Introduction
- 1.1 Abstract Functions
- 1.2 The Mean Value Theorem
- 1.3 The Riemann Integral Abstract Functions
- 1.4 Abstract Lebesgue Integrals
- 1.5 The Abstract Stieltjes Integral
- 1.6 Gateaux and Fréchet Differentials
- 1.7 Notes
- Chapter 2. Semigroups of Operators
- 2.0 Introduction
- 2.1 Strongly Continuous Semigroups of Operators
- 2.2 The Infinitesimal Generator
- 2.3 The Hille-Yosida-Phillips Theorem
- 2.4 Linear Autonomous Funtional Differential Equations
- 2.5 Analytic Semigroups
- 2.6 Notes
- Chapter 3. Linear Evolution Equations of the Parabolic Type: Sobolevski-Tanabe Theory
- 3.0 Introduction
- 3.1 Definitions and Hypotheses
- 3.2 Statements of the Main Theorems and Some Heuristic Arguments
- 3.3 Properties of the Semigroup {exo[-tA(t)]}
- 3.4 Existence of a Fundamental Solution
- 3.5 Uniqueness of the Fundamental Solution
- 3.6 Solution of the Abstract Cauchy Problem
- 3.7 Differentiability of Solutions
- 3.8 Asymptotic Behavior
- 3.9 Notes
- Chapter 4. Evolution Inequalities
- 4.0 Introduction
- 4.1 Lower Bounds, Uniqueness, and Convexity (Special Results)
- 4.2 Lower Bounds, Uniqueness, and Convexity (General Results)
- 4.3 Approximate Solutions, Bounds, and Uniqueness
- 4.4 Application to Parabolic Equations
- 4.5 Notes
- Chapter 5. Nonlinear Differential Equations
- 5.0 Introduction
- 5.1 Counterexamples
- 5.2 Existence and Uniqueness
- 5.3 Nonlinear Variation of Constants Formula
- 5.4 Stability and Asymptotic Behavior
- 5.5 Chaplygin's Method
- 5.6 Global Existence and Asymptotic Equilibrium
- 5.7 Lyapunov Functions and Stability Criteria
- 5.8 Notes
- Chapter 6. Special Topics
- 6.0 Introduction
- 6.1 Nonlinear Semigroups and Differential Equations
- 6.2 Functional Differential Equations in Banach Spaces
- 6.3 Second-Order Evolution Equations
- 6.4 Notes
- Appendixes
- Bibliography
- Index
