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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."
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John Holmes
reviewed Singular nonlinear partial differential equations on October 29, 2016
Singular nonlinear partial differential equations
The name of the story that I read is "How Serval Got His Spots" and since this is a fable, there isn't a author. This fable was told by the Ndebele people which is a community of people in Africa. The genre of this book is Folklore and the sub genre of this story is Fables. I chose to read this story for my English Presentation, since our unit is about fables. This particular story is retold by Nick Greaves.
This story explains how Servals got their spots. The setting of this book is In Africa, a long time ago. The central characters are a Serval and a snake. In this fable, Servals had no spots, and therefore were called 'Lion's Little Cousins'. Servals wished nothing but to have a beautiful coat like a Zebra. Then, one day when a snake got sick and no one else would help him, Serval was so nice to help him get better. To thank this act of kindness, the snake bit the Serval, and gave him spots.
This story teaches me a lesson about being kind and helpful. The Serval helped the snake when he was sick and no one else would help him. Also I think this story teaches that you should be kind to others, or else not many people will offer to help you when you need help. I liked this story because I think it teaches you important lessons. Since this is a fable, the characters didn't seem real. (Animals can talk) All in all, I liked this story.
10 - 13
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