| 书目名称 | Singular Nonlinear Partial Differential Equations | | 编辑 | Raymond Gérard,Hidetoshi Tahara | | 视频video | | | 丛书名称 | Aspects of Mathematics | | 图书封面 |  | | 描述 | 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 equ | | 出版日期 | Book 1996 | | 关键词 | Maillet‘s type theorems; differential equation; holomorphic solutions; non linear singular partial diff | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-322-80284-2 | | isbn_softcover | 978-3-322-80286-6 | | isbn_ebook | 978-3-322-80284-2Series ISSN 0179-2156 | | issn_series | 0179-2156 | | copyright | Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden 1996 |
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发表于 2025-3-21 19:19:51
