Das Anliegen dieser mathematischen Monographie ist die Zusammenfassung aller Resultate, die heutzutage vorliegen über die Existenz formaler, holomorpher oder singulärer Lösungen von singulären nicht-linearen partiellen Differentialgleichungen.
Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.
Prof. Raymond Gerard ist am Institut de Recherche Mathématique Alsacien an der Université Louis Pasteur in Strasbourg beschäftigt. Prof. Hidetoshi Tahara lehrt an der Sophia Universität in Tokyo.
Le informazioni nella sezione "Su questo libro" possono far riferimento a edizioni diverse di questo titolo.
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Paperback. Condizione: new. Paperback. 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. 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Codice articolo 9783322802866
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Da: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Germania
Taschenbuch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 272 pp. Englisch. Codice articolo 9783322802866
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