Description
Dover Stability Theory of Differential Equations 2008 Edition by Richard Bellman
Suitable for advanced undergraduates and graduate students, this was the first English-language text to offer detailed coverage of boundedness, stability, and asymptotic behavior of linear and nonlinear differential equations. It remains a classic guide, featuring material from original research papers, including the author's own studies.The linear equation with constant and almost-constant coefficients receives in-depth attention that includes aspects of matrix theory. No previous acquaintance with the theory is necessary, since author Richard Bellman derives the results in matrix theory from the beginning. In regard to the stability of nonlinear systems, results of the linear theory are used to drive the results of Poincaré and Liapounoff. Professor Bellman then surveys important results concerning the boundedness, stability, and asymptotic behavior of second-order linear differential equations. The final chapters explore significant nonlinear differential equations whose solutions may be completely described in terms of asymptotic behavior. Only real solutions of real equations are considered, and the treatment emphasizes the behavior of these solutions as the independent variable increases without limit. Table of contents :- Preface1. Properties of Linear Systems2. Stability, Boundedness, and Asymptotic Behavior of Solutions of Linear Systems3. The Existence and Uniqueness of Solutions of Nonlinear Systems4. The Stability of Solutions of Nonlinear Differential Equations5. The Asymptotic Behavior of the Solutions of Some Nonlinear Equations of the First Order6. The Second-order Linear Differential Equation7. The Emden-Fowler EquationIndex