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Titlebook: Basic Theory of Ordinary Differential Equations; Po-Fang Hsieh,Yasutaka Sibuya Textbook 1999 Springer Science+Business Media New York 1999

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期刊全称Basic Theory of Ordinary Differential Equations
影响因子2023Po-Fang Hsieh,Yasutaka Sibuya
视频videohttp://file.papertrans.cn/182/181179/181179.mp4
学科分类Universitext
图书封面Titlebook: Basic Theory of Ordinary Differential Equations;  Po-Fang Hsieh,Yasutaka Sibuya Textbook 1999 Springer Science+Business Media New York 1999
影响因子The authors‘ aim is to provide the reader with the very basic knowledge necessary to begin research on differential equations with professional ability. The selection of topics should provide the reader with methods and results that are applicable in a variety of different fields. The text is suitable for a one-year graduate course, as well as a reference book for research mathematicians. The book is divided into four parts. The first covers fundamental existence, uniqueness, smoothness with respect to data, and nonuniqueness. The second part describes the basic results concerning linear differential equations, the third deals with nonlinear equations. In the last part the authors write about the basic results concerning power series solutions. Each chapter begins with a brief discussion of its contents and history. The book has 114 illustrations and 206 exercises. Hints and comments for many problems are given.
Pindex Textbook 1999
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Asymptotic Solutions in a Parameter,In this chapter, we explain asymptotic solutions of a system of differential equations.In §§XII-1, XII-2, and XII-3, existence of such asymptotic solutions in the sense of Poincaré is proved in detail. In §XII-4, this result is used to prove a block-diagonalization theorem of a linear system
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https://doi.org/10.1007/978-3-030-66792-4I-1. Topological properties of a set covered by solution curves of problem (P) are explained in §§III-2 and III-3. The main result is the Kneser theorem (Theorem III-2-4, cf. [Kn]). In §III-4, we explain maximal and minimal solutions and their continuity with respect to data. In §§III-5 and III-6, u
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