| Popis: |
In this chapter, we explain asymptotic solutions of a system of differential equations \({{\epsilon }^{\sigma }}\frac{{d\vec{y}}}{{dx}} = \vec{f}\left( {x,\vec{y},\epsilon } \right){\text{ as }}\epsilon \to 0\) In §§XII-1, XII-2, and XII-3, existence of such asymptotic solutions in the sense of Poincare is proved in detail. In §XII-4, this result is used to prove a block-diagonalization theorem of a linear system \({ \in ^\sigma }\frac{{d\mathop {{\text{ }}y}\limits^ \to }}{{dx}} = A(x, \in )\vec y. \) |
