Nonlinear Differential Equations

This concise and widely referenced monograph has served as a text for generations of advanced undergraduate math majors and graduate students. Prepared with an eye toward the needs of applied mathematicians, engineers, and physicists, the treatment is equally valuable as a reference for professionals.
After discussing some mathematical preliminaries, author Raimond A. Struble presents detailed treatments of the existence and the uniqueness of a solution of the initial-value problem, properties of solutions, properties of linear systems, stability in nonlinear systems, and two-dimensional systems. Additional chapters examine perturbations of periodic solutions and a general asymptotic method. Numerous exercises appear throughout the book, along with examples that contribute additional material, illustrate theorems and concepts, and provide a link with more practical aspects of the theory.

Raimond A. Struble (1923–2013) was on the faculty of North Carolina State University from 1958 until his retirement in 1987. In addition to Nonlinear Differential Equations, he was the author of over 70 articles published in the mathematical literature. Nonlinear Differential Equations is a widely referenced text and was translated into several foreign languages.

Preface1. Preliminary Considerations2. The Existence and the Uniqueness of a Solution of the Initial-Value Problem3. Properties of Solutions4. Properties of Linear Systems5. Stability in Nonlinear Systems6. Two-Dimensional Systems7. Perturbations of Periodic Solutions8. A General Asymptotic MethodGeneral ReferencesIndex