Bifurcation Theory: An Introduction with Applications to Partial Differential Equations

This book is a valuable resource for mathematicians working in the areas of Nonlinear Analysis and/or Differential Equations. It consists of three chapters, namely “Local Theory,” “Global Theory” and “Applications.” The first two chapters are an exposition of a wide variety of theoretical results, many of which are rarely presented together in the classical books on the subject. The third chapter contains applications to problems originating in Physics, focusing on the application of the theory rather than the modeling and the derivation of the differential equations.

This book is intended for advanced graduate students, for specialists in Bifurcation Theory and for researchers in related areas willing to master the subject. Undergraduate and beginning graduate students will probably find the book difficult to read due to the demanding prerequisites from Functional Analysis and to the lack of exercises. The absence of exercises also makes it harder for instructors to use it as a sole text in a course on Bifurcation Theory.

The book more than makes up for this, however, through the rich variety of sub-topics in each chapter and by the inclusion of recent results. All the prerequisites are very well documented with precise references to the literature and the adventurous reader will be delighted by the clarity of the material and by the Notes and Remarks spread throughout the text and at the end of each chapter. In conclusion, this is a great reference book on the subject of Bifurcations.

Florin Catrina is Assistant Professor of Mathematics at St. John's University in Queens, New York.