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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General Theory of Linear Systems,ued) continuous functions of a real independent variable ., and the?.-valued function.is continuous in . The existence and uniqueness of solutions of problem (LP) were given by Theorem I-3-5. In §IV-1, we explain some basic results concerning n x n matrices whose entries are complex numbers. In part

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Boundary-Value Problems of Linear Differential Equations of the Second-Order,roblems (§§VI2—VI-4, topics including Green’s functions, self-adjointness, distribution of eigen-values, and eigenfunction expansion), (3) scattering problems (§§VI-5—VI-9, mostly focusing on reflectionless potentials), and (4) periodic potentials (§VI-10). The materials concerning these topics are

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Stability,tems. To start with, in §VIII-1, we introduce the concepts of stability and asymptotic stability of a given particular solution as ..We illustrate those concepts with simple examples. Reducing the given solution to the trivial solution by a simple transformation, we concentrate our explanation on th

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The Second-Order Differential Equation ,ndedness of solutions and apply these results to the van der Pol equation.(cf. Example X-2–5). The boundedness of solutions and the instability of the unique stationary point imply that the van der Pol equation has a nontrivial periodic solution. This is a consequence of the Poincaré-Bendixson Theor

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Asymptotic Expansions,mple, as we mentioned it in Remark V-1-4, the divergent formal power series.is a formal solution of ..This equation has an actual solution .Integrating by parts,we obtain. Since.we conclude that.an asymptotic representation of an actual solution by means of a formal solution. In this chapter, we exp