書中主要講解了微分方程理論的基本方法，對微分方程的存在性、連續(xù)依賴性、穩(wěn)定性、周期解、自治微分系統(tǒng)、動力系統(tǒng)等基本問題進行詳細分析，并注重理論間的聯(lián)系。《微分方程的定性理論》基礎(chǔ)性強、應(yīng)用廣泛，是一本適合大學(xué)高年級選修課、研究生雙語教學(xué)以及讀者自學(xué)的英文教科書。
是一本適合大學(xué)高年級選修課、研究生雙語教學(xué)以及讀者自學(xué)的英文教科書。
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
The study of linear differential equations is very important for the fol-lowing reasons. First， the study provides us with some basic knowledgefor understanding general nonlinear differential equations. Second， manynonlinear differential equations can be written as summations of linear dif-ferential equations and some small nonlinear perturbations. Thus， undercertain conditions， the qualitative properties of linear differential equationscan be used to infer essentially the same qualitative properties for nonlineardifferential equations.
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