AVANT
发表于 2025-3-28 16:18:06
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 . The main topic of §XIII-5 is
厚颜
发表于 2025-3-28 19:48:14
http://reply.papertrans.cn/19/1812/181179/181179_42.png
Genome
发表于 2025-3-29 00:19:48
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
发表于 2025-3-29 04:37:47
http://reply.papertrans.cn/19/1812/181179/181179_44.png
conception
发表于 2025-3-29 09:36:38
http://reply.papertrans.cn/19/1812/181179/181179_45.png
Arroyo
发表于 2025-3-29 13:26:16
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
发表于 2025-3-29 16:42:07
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
发表于 2025-3-29 23:05:45
Singularities of the Second Kind,n and . 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. ). In §XIII-8, we explain asymptotic solutions in the Gevrey asymptotics. To understand ma
欢乐中国
发表于 2025-3-30 00:12:42
http://reply.papertrans.cn/19/1812/181179/181179_49.png
不安
发表于 2025-3-30 06:28:44
R. J. Geretshauser,R. Speith,W. Kleyeal] and the existence and uniqueness Theorem I-1-4 is due to É. Picard and E. Lindelöf . 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