Preface
 Chapter Ⅰ.Fundamental Theorems of Ordinary Differential Equations
  Ⅰistence and uniqueness with the Lipschitz condition
  Ⅰistence without the Lipschitz condition
  Ⅰme global properties of solutions
  Ⅰalytic differential equations
  Exercises Ⅰ
 Chapter Ⅱ.Dependence on Data
  Ⅱntinuity with respect to initial data and parameters
  Ⅱfferentiability
  Exercises Ⅱ
 Chapter Ⅲ. Nonuniqueness
  Ⅲamples
  Ⅲe Kneser theorem
  Ⅲlution curves on the boundary of R(A)
  Ⅲximal and minimal solutions
  Ⅲ-5.A comparison theorem
  Ⅲfficient conditions for uniqueness
  Exercises Ⅲ
 Chapter Ⅳ. General Theory of Linear Systems
  Ⅳme basic results concerning matrices
  Ⅳmogeneous systems of linear differential equations
  Ⅳmogeneous systems with constant coefficients
  Ⅳstems with periodic coefficients
  Ⅳnear Hamiltonian systems with periodic coefficients
  Ⅳnhomogeneous equations
  Ⅳgher-order scalar equations
  Exercises Ⅳ
 Chapter Ⅴ. Singularities of the First Kind
  Ⅴrmal solutions of an algebraic differential equation
  Ⅴnvergence of formal solutions of a system of the first kind
  Ⅴe S-N decomposition of a matrix of infinite order
  Ⅴe S-N decomposition of a differential operator
  Ⅴ-5.A normal form of a differential operator
  Ⅴlculation of the normal form of a differential operator
  Ⅴassification or singularities of homogeneous linear systems
  Exercises Ⅴ
 Chapter Ⅵ.Boundary-Value Problems of Linear Differential Equations of the Second-Order
  Ⅵros of solutions
  Ⅵurm-Liouville problems
  Ⅵgenvalue problems
  Ⅵgenfunction expansions
  Ⅵst solutions
  Ⅵattering data
  Ⅵffectionless potentials
  Ⅵnstruction of a potential for given data
  Ⅵfferential equations satisfied by reflectionless potentials
  Ⅵriodic potentials
  Exercises Ⅵ
 Chapter Ⅶ.Asymptotic Behavior of Solutions of Linear Systems
  Ⅶapounoff’s type numbers
  Ⅶapounoff’s type numbers of a homogeneous linear system
  Ⅶlculation of Liapounoff’s type numbers of solutions
  Ⅶ-4.A diagonalization theorem
  Ⅶstems with asymptotically constant coefficients
  Ⅶ application of the Floquet theorem
  Exercises Ⅶ
 Chapter Ⅷ.Stability
  Ⅷsic definitions
  Ⅷ-2.A sufficient condition for asymptotic stability
  Ⅷable manifolds
  Ⅷalytic structure of stable manifolds
  Ⅷo-dimensional linear systems with constant coefficients
  Ⅷalytic systems in R2
  Ⅷrturbations of an improper node and a saddle point
  Ⅷrturbations of a proper node
  Ⅷrturbation of a spiral point
  Ⅷrturbation of a center
  Exercises VIII
 Chapter Ⅸ.Autonomous Systems
  Ⅸmit-invariant sets
  Ⅸapounoff’s direct method
  Ⅸbital stability
  Ⅸe Poincaré-Bendixson theorem
  Ⅸdices of Jordan curves
  Exercises Ⅸ
 Chapter Ⅹ.The Second-Order Differential Equationd2x/dt2+h(x)dx/dt+g(x)=0
  Ⅹo-point boundary-value problems
  Ⅹplications of the Liapounoff functions
  Ⅹistence and uniqueness of periodic orbits
  Ⅹltipliers of the periodic orbit of the van der Pol equation
  Ⅹe van der Pol equation for a smallε＞0
  Ⅹe van der Pol equation for a large parameter
  Ⅹ-7.A theorem due to M. Nagumo
  Ⅹ-8.A singular perturbation problem
  Exercises Ⅹ
 Chapter Ⅺ.Asymptotic Expansions
  Ⅺymptotic expansions in the sense of Pomcaré
  Ⅺvrey asymptotics
  Ⅺat functions in the Gevrey asymptotics
  Ⅺsic properties of Gevrey asymptotic expansions
  Ⅺof of Lemma XI-2-6
  Exercises XI
 Chapter Ⅻ.Asymptotic Expansions in a Parameter
  Ⅻ existence theorem
  Ⅻsic estimates
  Ⅻof of Theorem Ⅻ-1-2
  Ⅻ-4.A block-diagonalization theorem
  Ⅻvrey asymptotic solutions in a parameter
  Ⅻalytic simplification in a parameter
  Exercises Ⅻ
 Chapter ⅫⅠ.Singularities of the Second Kind
  ⅫⅠ existence theorem
  ⅫⅠsic estimates
  ⅫⅠof of Theorem ⅫⅠ-1-2
  ⅫⅠ-4.A block-diagonalization theorem
  ⅫⅠclic vectors (A lemma of P. Deligne)
  ⅫⅠe Hukuhara-Tbrrittin theorem
  ⅫⅠ n-th-order linear differential equation at a singular point of the second kind
  ⅫⅠvrey property of asymptotic solutions at an irregular singular point
  Exercises ⅫⅠ
 References
 Index