Qualitative Theory of Differential Equations

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 Poincare-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 book would be accessible to graduate students and advanced undergraduates and would also be of interest to researchers in this area.

Exercises are included at the end of each chapter.