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Nonlinear Differential Equations【2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载】

Nonlinear Differential Equations
  • Raimond A.Struble 著
  • 出版社： Inc.
  • ISBN：
  • 出版时间：1962
  • 标注页数：267页
  • 文件大小：48MB
  • 文件页数：276页
  • 主题词：

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图书目录

CHAPTER 1 PRELIMINARY CONSIDERATIONS1

1．Linear Second-order Equations1

2．Some Nonlinear Second-order Equations16

3．The Initial-value Problem25

4．Higher-order Systems28

5．The Taxicab Geometry35

6．Continuous,Differentiable,Analytic,and Lipschitz Vector Functions38

CHAPTER 2 THE EXISTENCE AND THE UNIQUENESS OF A SOLUTION OF THE INITIAL-VALUE PROBLEM41

1．The Cauchy-Lipschitz Existence Theorem41

2．The Uniqueness Theorem46

3．Continuity with Respect to Initial Values48

4．The Cauchy-Peano Existence Theorem49

5．An Existence and Uniqueness Theorem for Nonautonomous Systems56

CHAPTER 3 PROPERTIES OP SOLUTIONS60

1．Extension of the Trajectories60

2．Continuity Properties of Trajectories62

3．The Poincaré Expansion Theorem67

4．Differentiability of Solutions72

CHAPTER 4 PROPERTIES OF LINEAR SYSTEMS79

1．Bases and the Principal Matrix Solution79

2．The Linear Inhomogeneous Equation91

3．Linear Homogeneous Equations with Constant Coefficients98

4．Linear Systems with Periodic Coefficients106

5．Asymptotic Behavior of Solutions of Linear Systems115

CHAPTER 5 STABILITY IN NONLINEAR SYSTEMS129

1．The Concept of Stability129

2．Stability of Singular Points of Autonomous Systems131

3．Stability of Singular Points of Nonautonomous Systems137

4．Stability of Singular Solutions of Implicit Equations144

5．Stability of Nonsingular Solutions149

6．Direct Stability Method160

CHAPTER 6 TWO-DIMENSIONAL SYSTEMS170

1．Critical Points of Autonomous Systems170

2．Properties of Limit Cycles179

CHAPTER 7 PERTURBATIONS OF PERIODIC SOLUTIONS194

1．Perturbations of Periodic Solutions in Non-autonomous Systems194

2．Periodic Solutions of Nonautonomous Quasi-harmonic Equations203

3．Perturbations of Periodic Solutions in Autonomous Systems209

4．Periodic Solutions of Autonomous Quasi-harmonic Equations215

CHAPTER 8 A GENERAL ASYMPTOTIC METHOD220

1．Introduction220

2．The Mathieu Equation221

3．The Free Oscillations of the van der Pol Equation236

4．The Forced Oscillations of the van der Pol Equation240

5．The Forced Oscillations of the Duffing Equation251

GENERAL REFERENCES262

Index263

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