Ordinary differential equations : introduction and qualitative theory

Prefaces  Introduction    Existence Theorems  What This Chapter Is About   Existence Theorem by Successive Approximations  Differentiability Theorem  Existence Theorem for Equation with a Parameter  Existence Theorem Proved by Using a Contraction Mapping  Existence Theorem without Uniqueness   Extension Theorems  Examples    Linear Systems  Existence Theorems for Linear Systems  Homogeneous Linear Equations: General Theory  Homogeneous Linear Equations with Constant Coefficients   Homogeneous Linear Equations with Periodic Coefficients: Floquet Theory  Inhomogeneous Linear Equations  Periodic Solutions of Linear Systems with Periodic Coefficients  Sturm-Liouville Theory    Autonomous Systems  Introduction   General Properties of Solutions of Autonomous Systems   Orbits near an Equilibrium Point: The Two-Dimensional Case  Stability of an Equilibrium Point  Orbits near an Equilibrium Point of a Nonlinear System  The Poincare-Bendixson Theorem  Application of the Poincare-Bendixson Theorem    Stability  Introduction   Definition of Stability   Examples  Stability of Solutions of Linear Systems   Stability of Solutions of Nonlinear Systems   Some Stability Theory for Autonomous Nonlinear Systems   Some Further Remarks Concerning Stability    The Lyapunov Second Method   Definition of Lyapunov Function  Theorems of the Lyapunov Second Method  Applications of the Second Method    Periodic Solutions  Periodic Solutions for Autonomous Systems   Stability of the Periodic Solutions  Sell's Theorem   Periodic Solutions for Nonautonomous Systems    Perturbation Theory: The Poincare Method   Introduction  The Case in which the Unperturbed Equation Is Nonautonomous and Has an Isolated Periodic Solution  The Case in which the Unperturbed Equation Has a Family of Periodic Solutions: The Malkin-Roseau Theory  The Case in which the Unperturbed Equation Is Autonomous    Perturbation Theory: Autonomous Systems and Bifurcation Problems   Introduction    Using the Averaging Method: An Introduction  Introduction  Periodic Solutions   Almost Periodic Solutions    Appendix  Ascoli's Theorem   Principle of Contraction Mappings   The Weierstrass Preparation Theorem  Topological Degree    References  Index    Exercises appear at the end of each chapter.