PageHeader : Funkcialaj Ekvacioj, 16 (1973), 103-136
Title : A General Solution of a System of Nonlinear
Title : Differential Equations at an IrreguIar
Title : Type Singu1arity*
AuthorInfo : (Dedicated to Professor Hugh L. Turrittin on his retirement)
AuthorInfo : By Po-Fang HSIEH
AuthorInfo : (Western Michigan University)
section : I. INTRODUCTION
subsection : 1. Briot-Bouquet type singularity.
subsection : 2. Irregular type singularity.
subsection : 3. Notations and definitions.
subsection : 4. Statement of problems.
subsection : 5. Preliminary reductions.
subsection : 6. Main assumptions and reductions.
subsection : 7. A general solution.
section : II. EXISTENCE THEOREMS
subsection : 8. First existence theorem.
subsection : 9. Second existence theorem.
section : III. PROOF OF THEOREM 1
subsection : 10. A particular solution and its reduction.
subsection : 11. A block-diagonalization theorem and proof of Theorem 1.
subsection : 12. Proof of Theorem 1. 2.
section : IV. PROOF OF THEOREM 2.
subsection : 13. Differential equations for $R_{j}$ and $S$ .
subsection : 14. Solutions $R_{j}(x, V(x))$ .
subsection : 15. The solution $S(x, V(x))$ .
section : V. PROOF OF THEOREM 3?FORMAL TRANSFORMATION
subsection : 16. The equations for $A_{p}$ and $B_{p}$ .
subsection : 17. The functions $A_{p}$ and $B_{p}$ .
section : VI. PROOF OF THEOREM 3?ANALYTIC TRANSFORMATION
subsection : 18. A fundamental lemma.
subsection : 19. Proof of Lemma 3. 1.
subsection : 20. A theorem to prove the convergence.
subsection : 21. Proof of Theorem 3. 1.
section : References