Gérard, R. (Raymond) 1932
Overview
Works:  28 works in 128 publications in 3 languages and 1,253 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor, Thesis advisor, Compiler, Other 
Classifications:  QA3, 510 
Publication Timeline
.
Most widely held works by
R Gérard
Equations différentielles et systèmes de Pfaff dans le champ complexe by
R Gérard(
Book
)
56 editions published between 1979 and 2008 in 4 languages and held by 631 WorldCat member libraries worldwide
56 editions published between 1979 and 2008 in 4 languages and held by 631 WorldCat member libraries worldwide
Singular nonlinear partial differential equations by
R Gérard(
Book
)
12 editions published between 1996 and 2012 in English and Undetermined and held by 135 WorldCat member libraries worldwide
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
12 editions published between 1996 and 2012 in English and Undetermined and held by 135 WorldCat member libraries worldwide
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
Théorie de Fuchs sur une varieté analytique complexe by
R Gérard(
Book
)
11 editions published between 1968 and 1969 in French and Undetermined and held by 32 WorldCat member libraries worldwide
11 editions published between 1968 and 1969 in French and Undetermined and held by 32 WorldCat member libraries worldwide
Oeuvres de Paul Painlevé. [Leçons sur la théorie analytique des équations différentielles] : [professées à Stockholm] by
Paul Painlevé(
Book
)
5 editions published between 1972 and 1973 in French and held by 22 WorldCat member libraries worldwide
5 editions published between 1972 and 1973 in French and held by 22 WorldCat member libraries worldwide
Œuvres de Paul Painlevé by
Paul Painlevé(
Book
)
4 editions published in 1975 in French and held by 21 WorldCat member libraries worldwide
4 editions published in 1975 in French and held by 21 WorldCat member libraries worldwide
Œuvres de Paul Painlevé by
Paul Painlevé(
Book
)
3 editions published in 1974 in French and held by 20 WorldCat member libraries worldwide
3 editions published in 1974 in French and held by 20 WorldCat member libraries worldwide
Journées complexes de Metz, février 1972 : [équations différentielles et fonctions de plusieurs variables(
Book
)
2 editions published in 1973 in French and held by 17 WorldCat member libraries worldwide
2 editions published in 1973 in French and held by 17 WorldCat member libraries worldwide
Analyse et équations différentielles du premier ordre : <travaux classés dans l'ordre chronologique> 1886  1902 by
Paul Painlevé(
Book
)
2 editions published in 1974 in French and held by 9 WorldCat member libraries worldwide
2 editions published in 1974 in French and held by 9 WorldCat member libraries worldwide
Holomorphic and singular solutions of nonlinear singular first order partial differential equations by
R Gérard(
Book
)
3 editions published in 1990 in English and held by 7 WorldCat member libraries worldwide
3 editions published in 1990 in English and held by 7 WorldCat member libraries worldwide
Solutions holomorphes et singulières d'équations aux dérivées partielles singulières non linéaires by
R Gérard(
Book
)
1 edition published in 1991 in French and held by 7 WorldCat member libraries worldwide
1 edition published in 1991 in French and held by 7 WorldCat member libraries worldwide
Convergent factorial series solutions of singular operator equations by
R Gérard(
Book
)
3 editions published in 1988 in English and held by 6 WorldCat member libraries worldwide
3 editions published in 1988 in English and held by 6 WorldCat member libraries worldwide
Maillet's type theorems for non linear singular partial differential equations without linear part by
R Gérard(
Book
)
2 editions published in 1990 in English and held by 6 WorldCat member libraries worldwide
2 editions published in 1990 in English and held by 6 WorldCat member libraries worldwide
Formal reduction of integrable linear connexion having a certain kind of irregular singularities by
H Charrier(
Book
)
4 editions published in 1980 in English and Undetermined and held by 6 WorldCat member libraries worldwide
4 editions published in 1980 in English and Undetermined and held by 6 WorldCat member libraries worldwide
Opérateurs non linéaires à singularité régulière, cas d'une variable by
R Gérard(
Book
)
1 edition published in 1989 in French and held by 6 WorldCat member libraries worldwide
1 edition published in 1989 in French and held by 6 WorldCat member libraries worldwide
Recent advances in cardiac arrhythmias(
Book
)
2 editions published in 1983 in Undetermined and English and held by 5 WorldCat member libraries worldwide
2 editions published in 1983 in Undetermined and English and held by 5 WorldCat member libraries worldwide
Sur l'indice des opérateurs différentiels ordinaires by
Kamel Betina(
Book
)
1 edition published in 1978 in French and held by 5 WorldCat member libraries worldwide
1 edition published in 1978 in French and held by 5 WorldCat member libraries worldwide
Maillet's type theorems for non linear singular partial differential equations by
R Gérard(
Book
)
3 editions published in 1990 in English and held by 5 WorldCat member libraries worldwide
3 editions published in 1990 in English and held by 5 WorldCat member libraries worldwide
Asymptotic implicit function theorems by
R Gérard(
Book
)
in French and English and held by 4 WorldCat member libraries worldwide
in French and English and held by 4 WorldCat member libraries worldwide
Formal and convergent solutions of singular partial differential equations by
Gunter Bengel(
Book
)
1 edition published in 1982 in English and held by 4 WorldCat member libraries worldwide
1 edition published in 1982 in English and held by 4 WorldCat member libraries worldwide
I. Déformations localement isoirrégulières de connexions linéraires complètement intégrables sur P [indice m] (C)
; II. Classification topologique de nuples de champs de vecteurs holomorphes commutatifs sur P [indice n+1] (C) by
Bernard Klarès(
Book
)
1 edition published in 1980 in French and held by 4 WorldCat member libraries worldwide
1 edition published in 1980 in French and held by 4 WorldCat member libraries worldwide
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Audience Level
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Related Identities
 Ramis, J.P (JeanPierre) Other Author Editor
 Centre national de la recherche scientifique (France) Editor
 Institut de recherche mathématique avancée
 Tahara, Hidetoshi
 Sec, Antoinette Compiler Editor
 Painlevé, Paul (18631933) Author
 Reeb, Georges Compiler Editor
 SpringerLink (Service en ligne)
 Institut de recherche mathématique avancée (Strasbourg) Editor
 Garnier, René 18871984 Author of introduction
Associated Subjects