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

AVANT

Singularities of the Second Kind,III-1,XIII-2, and XIII-3, a basic existence theorem of 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. The materials in §§XIII-1—XIII-4 are also found in [Si7]. The main topic of §XIII-5 is

厚颜

Genome

General Theory of Linear Systems,fraction decomposition of reciprocal of the characteristic polynomial. It is relatively easy to obtain this decomposition with an elementary calculation if all eigenvalues of a given matrix are known (cf. Examples IV-1-18 and IV-1-19). In §IV-2, we explain the general aspect of linear homogeneous sy

ALE

conception

Arroyo

Stability,table manifolds more closely for analytic differential equations. First we change a given system by an analytic transformation to a simple standard form. By virtue of such a simplification, we can construct the stable manifold in a simple analytic form. This idea is applied to analytic systems in ℝ.

headway

The Second-Order Differential Equation ,d small. This is a typical problem of regular perturbations. In §X-6, we explain how to locate the unique periodic solution of (E) geometrically as..In §X-8, we explain how to find an approximation of the periodic solution of (E) analytically as..This is a typical problem of singular perturbations.

兴奋过度

Singularities of the Second Kind,n [Huk4] and [Tul]. In §XIII-7, the Newton polygon of a linear differential operator is defined. This polygon is useful when we calculate formal solutions of an n-th-order linear differential equation (cf. [St]). In §XIII-8, we explain asymptotic solutions in the Gevrey asymptotics. To understand ma

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不安

R. J. Geretshauser,R. Speith,W. Kleyeal] and the existence and uniqueness Theorem I-1-4 is due to É. Picard [Pi] and E. Lindelöf [Lindl, Lind2]. The extension of these local solutions to a larger interval is explained in §I-3, assuming some basic requirements for such an extension. In §I-4, using successive approximations, we explain