包邮常微分方程基础理论(影印版)

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.Liapounoff's type numbers
　Ⅶ-2.Liapounoff's type numbers of a homogeneous linear system
　Ⅶ-3.Calculation of Liapounoff's 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.Liapounoff's 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