Vieweg Aspects of Mathematics 1996; 269 pp; hardcover Volume: 28 ISBN10: 3528066598 ISBN13: 9783528066598 List Price: US$109 Member Price: US$98.10 Order Code: VWAM/28
 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, BriotBouquet type PDE, higher order nonlinear Fuchsian PDE, Poincaré's and Siegel's results for vector fields, and also a general form of the CauchyKowalewski 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 integrodifferential equations
 Bibliography
 Index
