PageHeader : Funkcialaj, Ekvacioj 10 (1967) , 75-105 Title : A Method to Construct Analytic Expressions Title : for Bounded Solutions of Non-linear Title : Ordinary Differential Equations Title : with an Irregular Title : Singular Point AuthorInfo : By Masahiro IWANO* AuthorInfo : (University of Minnesota and Tokyo Metropolitan University) subsubsection : 1. Introduction. section : CHAPTER I. THE EQUATION (A) subsection : Section I. Particular Solutions. subsubsection : 2. Formal solutions. subsubsection : 3. Analytical meaning of the formal solution (2. 6). subsection : Section II. Proof of Auxiliary Theorem I. subsubsection : 4. Fundamental inequalities. subsubsection : 5. Proof of the Proposition 4. 1. subsubsection : 6. Proof of Auxiliary Theorem I. section : CHAPTER II. THE EQUATION (B) subsubsection : 7. Formal solution. subsubsection : 8. Analytic meaning of the formal solution (7. 1). subsubsection : 9. Proof of Auxiliary Theorem II. subsubsection : 10. Proof of Proposition 9. 1. section : CHAPTER III. THE EQUATION (C). subsubsection : 11. Formal solution depending on (x,u). subsubsection : 12. Analytic meaning of the formal solution (11. 1). subsubsection : 13. Proof of Auxiliary Theorem III. subsubsection : 14. Determination of the function $\text{{\it {\bf \^{A}}}}(\varphi)$ . subsubsection : 15. Fundamental properties of the vector functions $\exp {\rm Re} \Lambda^{\hat}(x)$ subsubsection : 16. Solution of Main Problem III. section : References