Qualitative Theory of Differential Equations
About this Title
Zhang Zhi-fen, Ding Tong-ren, Huang Wen-zao and Dong Zhen-xi. Translated by Anthony W. Leung
Publication: Translations of Mathematical Monographs
Publication Year: 1992; Volume 101
ISBNs: 978-0-8218-4183-9 (print); 978-1-4704-4512-6 (online)
MathSciNet review: MR1175631
MSC: Primary 34-01; Secondary 34Axx, 34Cxx, 54H20, 58Fxx
This book provides an introduction to and a comprehensive study of the qualitative theory of ordinary differential equations. It begins with fundamental theorems on existence, uniqueness, and initial conditions, and discusses basic principles in dynamical systems and Poincaré-Bendixson theory. The authors present a careful analysis of solutions near critical points of linear and nonlinear planar systems and discuss indices of planar critical points. A very thorough study of limit cycles is given, including many results on quadratic systems and recent developments in China. Other topics included are: the critical point at infinity, harmonic solutions for periodic differential equations, systems of ordinary differential equations on the torus, and structural stability for systems on two-dimensional manifolds.
This books is accessible to graduate students and advanced undergraduates and is also of interest to researchers in this area. Exercises are included at the end of each chapter.
Graduate students and research mathematicians interested in differential equations.
Table of Contents
- Chapter I. Fundamental theorems
- Chapter II. Critical points on the plane
- Chapter III. Indices of planar critical points
- Chapter IV. Limit cycles
- Chapter V. Critical points at infinity
- Chapter VI. Harmonic solutions for two-dimensional periodic systems
- Chapter VII. Systems of ordinary differential equations on the torus
- Chapter VIII. Structural stability