Preface
Chapter Ⅰ.Fundamental Theorems of Ordinary Differential Equations
Ⅰ-1.Existence and uniqueness with the Lipschitz condition
Ⅰ-2.Existence without the Lipschitz condition
Ⅰ-3.Some global properties of solutions
Ⅰ-4.Analytic differential equations
Exercises Ⅰ

ChapterⅡ.Dependence on Data
Ⅱ-1.Continuity with respect to initial data and parameters
Ⅱ-2.Differentiability
Exercises Ⅱ

Chapter Ⅲ.Nonuniqueness
Ⅲ-1.Examples
Ⅲ-2.The Kneser theorem
Ⅲ-3.Solution curves on the boundary of R（A)
Ⅲ-4.Maximal and minimal solutions
Ⅲ-5.A comparison theorem
Ⅲ-6.Sufficient conditions for uniqueness
Exercises Ⅲ

Chapter Ⅳ.General Theory of Linear Systems
Ⅳ-1.Some basic results concerning matrices
Ⅳ-2.Homogeneous systems of linear differential equations
Ⅳ-3.Homogeneous systems with constant coefficients
Ⅳ-4.Systems with periodic coefficients
Ⅳ-5.Linear Hamiltonian systems with periodic coefficients
Ⅳ-6.Nonhomogeneous equations
Ⅳ-7.Higher-order scalar equations
Exercises Ⅳ

Chapter Ⅴ.Singularities of the First Kind
Ⅴ-1.Formal solutions of an algebraic differential equation
Ⅴ-2.Convergence of formal solutions of a system of the first kind
Ⅴ-3.The S-N decomposition of a matrix of infinite order
Ⅴ-4.The S-N decomposition of a differential operator
Ⅴ-5.A normal form of a differential operator
Ⅴ-6.Calculation of the normal form of a differential operator
Ⅴ-7.Classification of singularities of homogeneous linear systems
Exercises Ⅴ

Chapter Ⅵ.Boundary-Value Problems of Linear Differential Equations of the Second-Order
Ⅵ-1.Zeros of solutions
Ⅵ-2.Sturm-Liouville problems
Ⅵ-3.Eigenvalue problems
Ⅵ-4.Eigenfunction expansions
Ⅵ-5.Jost solutions
Ⅵ-6.Scattering data
Ⅵ-7.Refiectionless potentials
Ⅵ-8.Construction of a potential for given data
Ⅵ-9.Differential equations satisfied by reflectionless potentials
Ⅵ-10.Periodic potentials
Exercises Ⅵ

Chapter Ⅶ.Asymptotic Behavior of Solutions of Linear Systems
Ⅶ-1.Liapounoffs type numbers
Ⅶ-2.Liapounoffs type numbers of a homogeneous linear system
Ⅶ-3.Calculation of Liapounoffs type numbers of solutions
Ⅶ-4.A diagonalization theorem
Ⅶ-5.Systems with asymptotically constant coefficients
Ⅶ-6.An application of the Floquet theorem
Exercises Ⅶ

Chapter Ⅷ.Stability
Ⅷ-1.Basic definitions
Ⅷ-2.A sufficient condition for asymptotic stability
Ⅷ-3.Stable manifolds
Ⅷ-4.Analytic structure of stable manifolds
Ⅷ-5.Two-dimensional linear systems with constant coefficients
Ⅷ-6.Analytic systems in R2
Ⅷ-7.Perturbations of an improper node and a saddle point
Ⅷ-8.Perturbations of a proper node
Ⅷ-9.Perturbation of a spiral point
Ⅷ-10.Perturbation of a center
Exercises Ⅷ

Chapter Ⅸ.Autonomous Systems
Ⅸ-1.Limit-invariant sets
Ⅸ-2.Liapounoffs direct method
Ⅸ-3.Orbital stability
Ⅸ-4.The Poincare-Bendixson theorem
Ⅸ-5.Indices of Jordan curves
Exercises Ⅸ

Chapter Ⅹ.The Second-Order Differential Equation （d2x)/（dt2)+h（x)*（dx)/（dt)+g（x)=0
Ⅹ-1.Two-point boundary-value problems
Ⅹ-2.Applications of the Liapounoff functions
Ⅹ-3.Existence and uniqueness of periodic orbits
Ⅹ-4.Multipliers of the periodic orbit of the van der Pol equation
Ⅹ-5.The van der Pol equation for a small ε > 0
Ⅹ-6.The 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
Ⅺ-1.Asymptotic expansions in the sense of Poincare
Ⅺ-2.Gevrey asymptotics
Ⅺ-3.Flat functions in the Gevrey asymptotics
Ⅺ-4.Basic properties of Gevrey asymptotic expansions
Ⅺ-5.Proof of Lemma Ⅺ-2-6
Exercises Ⅺ

Chapter Ⅻ.Asymptotic Expansions in a Parameter
Ⅻ-1.An existence theorem
Ⅻ-2.Basic estimates
Ⅻ-3.Proof of Theorem Ⅻ-1-2
Ⅻ-4.A block-diagonalization theorem
Ⅻ-5.Gevrey asymptotic solutions in a parameter
Ⅻ-6.Analytic simplification in a parameter
Exercises Ⅻ

Chapter ⅩⅢ.Singularities of the Second Kind
ⅩⅢ-1.An existence theorem
ⅩⅢ-2.Basic estimates
ⅩⅢ-3.Proof of Theorem ⅩⅢ-1-2
ⅩⅢ-4.A block-diagonalization theorem
ⅩⅢ-5.Cyclic vectors （A lemma of P.Deligne)
ⅩⅢ-6.The Hukuhara-Turrittin theorem
ⅩⅢ-7.An n-th-order linear differential equation at a singular point of the second kind
ⅩⅢ-8.Gevrey property of asymptotic solutions at an irregular singular point
Exercises ⅩⅢ
References
Index