Singular Nonlinear Partial Differential Equations Paperback / softback
by Raymond Gerard, Hidetoshi Tahara
Part of the Aspects of Mathematics series
Paperback / softback
Description
The aim of this book is to put together all the results that are known about the existence of formal, holomorphic and singular solutions of singular non linear partial differential equations.
We study the existence of formal power series solutions, holomorphic solutions, and singular solutions of singular non linear partial differential equations.
In the first chapter, we introduce operators with regular singularities in the one variable case and we give a new simple proof of the classical Maillet's theorem for algebraic differential equations.
In chapter 2, we extend this theory to operators in several variables.
The chapter 3 is devoted to the study of formal and convergent power series solutions of a class of singular partial differential equations having a linear part, using the method of iteration and also Newton's method.
As an appli cation of the former results, we look in chapter 4 at the local theory of differential equations of the form xy' = 1(x,y) and, in particular, we show how easy it is to find the classical results on such an equation when 1(0,0) = 0 and give also the study of such an equation when 1(0,0) #- 0 which was never given before and can be extended to equations of the form Ty = F(x, y) where T is an arbitrary vector field.
Information
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Item not Available
- Format:Paperback / softback
- Pages:272 pages, biography
- Publisher:Springer Fachmedien Wiesbaden
- Publication Date:16/12/2011
- Category:
- ISBN:9783322802866
Other Formats
- PDF from £76.08
Information
-
Item not Available
- Format:Paperback / softback
- Pages:272 pages, biography
- Publisher:Springer Fachmedien Wiesbaden
- Publication Date:16/12/2011
- Category:
- ISBN:9783322802866
