"Differential equations, partial." . . "Singuläre Gleichung." . . "Reihenlösung" . . "Reihenlösung." . "Partial Differential Equations." . . "Singularität (Math.) Nichtlineare partielle Differentialgleichung." . . "Holomorphe Lösung" . . "Holomorphe Lösung." . "Niet-lineaire vergelijkingen." . . "Ecuaciones en derivadas parciales." . . "Nichtlineare partielle Differentialgleichung Formale Potenzreihe Reihenlösung." . . . . "Équations aux dérivées partielles." . . "Nichtlineare partielle Differentialgleichung Singuläre Lösung." . . "Nichtlineare partielle Differentialgleichung Singularität (Math.)" . . "Analysis." . . "Partiële differentiaalvergelijkingen." . . "Nichtlineare partielle Differentialgleichung Holomorphe Lösung." . . "Mathematics." . . "Global analysis (Mathematics)" . . "Formale Potenzreihe" . . "Formale Potenzreihe." . "Differential equations, Nonlinear Numerical solutions." . . "Singuläre Lösung" . . "Singuläre Lösung." . "Nichtlineare partielle Differentialgleichung" . . "Nichtlineare partielle Differentialgleichung." . . . . . . . . . "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."@en . . . . . . . . . . . . "Singular nonlinear partial differential equations" . . . "Singular Nonlinear Partial Differential Equations" . "Singular Nonlinear Partial Differential Equations"@en . . . . . . . . . "Electronic books"@en . . . . . . . . . . . . . . . . . . .