The main purpose of this book is to present all known results on the existence of formal, holomorphic, and singular solutions of singular nonlinear ordinary and partial differential equations in the complex domain. It contains a new approach to regular singularities for nonlinear PDE, Maillet type theorems for nonlinear PDE, Briot-Bouquet type PDE, higher order nonlinear Fuchsian PDE, Poincaré's and Siegel's results for vector fields, and also a general form of the Cauchy-Kowalewski theorem. Readers of the book are assumed to be familiar with only the basics on differential equations and function theory of complex variables.

A publication of Vieweg+Teubner. The AMS is exclusive distributor in North America. Vieweg+Teubner Publications are available worldwide from the AMS outside of Germany, Switzerland, Austria, and Japan.

Readership

Table of Contents

• Preface
• Operators with regular singularities: One variable case
• Operators with regular singularities: Several variables case
• Formal and convergent solutions of singular partial differential equations
• Local study of differential equations of the form \(xy^{\prime}=f(x,y)\) near \(x=0\)
• Holomorphic and singular solutions of non linear singular first order partial differential equations
• Maillet's type theorems for non linear singular partial differential equations
• Maillet's type theorems for non linear singular partial differential equations without linear part
• Holomorphic and singular solutions of non linear singular partial differential equations
• On the existence of holomorphic solutions of the Cauchy problem for non linear partial differential equations
• Maillet's type theorems for non linear singular integro-differential equations
• Bibliography
• Index