微分方程的定性理论

Preface

Chapter 1 A Brief Description

1. Linear Differential Equations

2. The Need for Qualitative Analysis

3. Description and Terminology

Chapter 2 Existence and Uniqueness

1. Introduction

2. Existence and Uniqueness

3. Dependence on Initial Data and Parameters

4. Maximal Interval of Existence

5. Fixed Point Method

Chapter 3 Linear Differential Equations

1. Introduction

2. General Nonhomogeneous Linear Equations

3. Linear Equations with Constant Coefficients

4. Periodic Coefficients and Floquet Theory

Chapter 4 Autonomous Differential Equations in R2

1. Introduction

2. Linear Autonomous Equations in R2

3. Perturbations on Linear Equations in R2

4. An Application： A Simple Pendulum

Chapter 5 Stability

1. Introduction

2. Linear Differential Equations

3. Perturbations on Linear Equations

4. Liapunovs Method for Autonomous Equations

Chapter 6 Periodic Solutions

1. Introduction

2. Linear Differential Equations

3. Nonlinear Differential Equations

Chapter 7 Dynamical Systems

1. Introduction

2. Poincare-Bendixson Theorem in R2

3. Limit Cycles

4. An Application： Lotka-Volterra Equation

Chapter 8 Some New Equations

1. Introduction

2. Finite Delay Differential Equations

3. Infinite Delay Differential Equations

4. Integrodifferential Equations

5. Impulsive Differential Equations

6. Equations with Nonlocal Conditions

7. Impulsive Equations with Nonlocal Conditions

8. Abstract Differential Equations

Appendix

References

Index

书中主要讲解了微分方程理论的基本方法，对微分方程的存在性、连续依赖性、稳定性、周期解、自治微分系统、动力系统等基本问题进行详细分析，并注重理论间的联系。《微分方程的定性理论》基础性强、应用广泛，是一本适合大学高年级选修课、研究生双语教学以及读者自学的英文教科书。