Ordinary Differential Equations and Stability Theory An Introduction

by Sanchez, David A.

• ISBN13: 9780486638287
• ISBN10: 0486638286
• Format: Paperback
• Copyright: 2012-02-29
• Publisher: Dover Publications

Summary

Beginning with a general discussion of the linear equation, topics developed include stability theory for autonomous and nonautonomous systems. Two appendices are also provided, and there are problems at the end of each chapter55 in all. Unabridged republication of the original (1968) edition. Appendices. Bibliography. Index. 55 problems.

Table of Contents

Introduction

Preliminary Notation

The Ordinary Differential Equation

An Existence and Uniqueness Theorem

The Maximum Interval of Existence Problems

The Linear Equation: General Discussion

Introduction

Fundamental Solutions

The Wronskian

The Nonhomogeneous Linear Equation

The nth-Order Linear Equation

The Nonhomogeneous nth-Order Linear Equation Problems

The Linear Equation with Constant Coefficients

The nth-Order Linear Equation

The Nonhomogeneous nth-Order Linear Equation

The Behavior of Solutions

The First-Order Linear System Problems

Autonomous Systems and Phase Space

Introduction

Linear Systems--Constant Coefficients

A General Discussion

Nonlinear Systems Problems

Stability for Nonautonomous Equations

Introduction

Stability for Linear Systems

Two Results for Nonlinear Systems

Liapunov's Direct Method

Some Results for the Second-Order Linear Equation Problems

Existence, Uniqueness, and Related Topics

Proof of the Existence and Uniqueness of Solutions

Continuation of Solutions and the Maximum Interval of Existence

The Dependence of Solutions on Parameters and Approximate Solutions Problems

Series Solutions of Second-Order Linear Equations

Linear Systems with Periodic Coefficients

References

Index

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