PageHeader : Funkcialaj Ekvacioj, 6 (1964), 89?141 Title : Asymptotic Solutions of a System of Linear Title : Ordinary Differential Equations Containing a Small Title : Parameter, II (Proof of the Fundamental Lemmas). AuthorInfo : By Masahiro IWANO AuthorInfo : (Tokyo Metropolitan University) section : 0. Introduction. section : Chapter IV. Proof of the fundamental lemmas subsection : Section I. Fundamental solution of the reduced form (VI). subsubsection : 1. Preliminaries. subsubsection : 2. Formal transformation. subsubsection : 3. Lemma. subsubsection : 4. Proof of Proposition 3. subsection : Section II. Formally blockly diagonalizing transformation of reduced forms (In), (IV) and (V). subsubsection : 5. Preliminary transformation. subsubsection : 6. Formally block-diagonalizing transformation. subsubsection : 7. Improvement of the result of Proposition 6 in the case when the coefficient matrix $D(x, \epsilon)$ of (5. 1) has a blockly triangular form. subsection : Section $\mathrm{I}\mathrm{I}\mathrm{I}$ . Problem of a system of nonlinear ordinary differential equations and fundamental lemmas. subsubsection : 8. Nonlinear differential equations. subsubsection : 9. Existence theorems and Lemmas 3, 4, 5. subsubsection : 10. Proof of the existence theorems. subsubsection : 11. Proof of Proposition 7. subsection : Section $\mathrm{I}\mathrm{V}$ . Determination of the paths of integration for reduced forms (III) and (V). subsubsection : 12. Preliminaries. subsubsection : 13. Determination of the domain $\mathfrak{D}^{*}(M_{0}^{\prime\prime}|\mathrm{e}|^{1/\mu} ; \Theta_{\pm}^{\prime\prime} ; a_{0}^{\prime\prime})$ and of the points $x_{j_{0}}$ . subsubsection : 14. Definition of the paths of integration $\Gamma jx_{0}$ and an auxiliary proposition. subsubsection : 15. Preliminaries. subsubsection : 16. Auxiliary proposition. subsection : Section V. Determination of the paths of integration for reduced form (IV). subsubsection : 17. Determination of a function $\Phi(\varphi)$ . section : References