PageHeader : Funkcialaj Ekvacioj, 38 (1995) 443-472
Title : New Study on the Convergence of a Formal Transformation
AuthorInfo : By
AuthorInfo : Masahiro IWANO
AuthorInfo : (Chuo University, Japan)
AuthorInfo : Dedicated to Professor Masuo Hukuhara on his eighty eighth birthday
section : 1. Introduction
subsection : 1o. Assumptions.
subsection : 2o. Review of some known works.
subsection : 3o. Main theorem.
section : 2. Formal transformation
subsection : 1o. Assumptions.
subsection : 2o. Formal transformation and simplified equations.
subsection : 3o. Proof.
subsection : 4o. Convergence of single power series.
section : 3. Special truncated differential equations
subsection : 1o. First transformation.
subsection : 2o. Second transformation.
subsection : 3o. New independent variable.
section : 4. Stable domains and the curve $\Gamma(x_{0})$
subsection : 1o. Stable domains.
subsection : 2o. The curve $\Gamma(x_{0})$ .
subsection : 3o. Stability theorem.
subsection : 4o. Proof of the case when x on $\Gamma^{\prime}$ .
section : 5. Verification of inequality (4.18): $\mathscr{F}(\sigma)>0$
section : 6. Existence of solution
subsection : 1o. Family of functions and mapping.
subsection : 2o. $\mathscr{T}\{\mathscr{F}\}\subset \mathscr{F}$ .
subsection : 3o. Verification of inequality (6.10-1) when $|\arg x_{\mathrm{o}}\mp\pi/2|\leq\pi/2-\Omega$ .
subsection : 4o. Verification of inequalities (6.10-1) and (6.10-2) when $\pi/2-\Omega\leq$ $|\arg x_{\mathrm{o}}\mp\pi/2|\leq\pi-\epsilon_{\mathrm{o}}$ .
subsection : 5o. Statement of Theorem.
subsection : 6o. Determination of various constants.
section : 7. Domain of holomorphy of the solutions
section : References