Masahiro Iwano

Intégration analytique d’un système d’équations différentielles non linéaires dans le voisinage d’un point singulier, I

RésuméNotre but est à rechercher, d’après la méthode de M. le Prof.Masuo Hukuhara, la signification analytique de la solution formelle, de (1.1), dépendant de quelconques constantes arbitraires.

Analytic expressions for bounded solutions of non-linear ordinary differential equations with an irregular type singular point

SummaryWe shall discuss how to construct analytic expressions for bounded solutions of non-linear ordinary differential equations of the form(A) which tend to0 as x approaches the origin along the positive real axis.

Analytic integration of a system of nonlinear ordinary differential equations with an irregular type singularity

SummaryWe shall discuss how to construct analytic expressions for bounded solutions of nonlinear ordinary differential equations of the form(A) which tend to0 with the order of certain positive powers of x as x approaches the origin through a sector. It will be shown that the opening angle of this sector is maximal.

On ann-parameter family of solutions of a nonlinearn-System with an irregular type singularity

SummaryThis paper discusses a nonlinear n-system of the form

A general solution of a system of nonlinear ordinary differential equationsxy′=f(x, y) in the case whenfy(0, 0) is the zero matrix

x^2 \frac{{dy}}{{dx}} = (1_n (\mu ) + x1_n (\alpha ))y + xf(x,y),

Analytic integration of a system of nonlinear ordinary differential equations with an irregular type singularity. - II

where the coefficient matrix of the linear part in y is an n-dimensional diagonal matrix and f(x, y) is an n-vector function holomorphic in (x, y) near the origin in the (x, y)-space. We assume that the diagonal matrix 1n(μ) has real diagonal components {μj} of signature (m, n−m), 1≦m≦n−1, and the real parts of the diagonal components {αj}, of the diagonal matrix 1n(α) are not necessarily positive numbers. If there exists a positive number χ satisfying the conditions

Applications of Nagumo-Hukuhara theory on the boundary value problems for nonlinear ordinary differential equations to abrikosov problem and Falkner-Skan problem

v_j (\varkappa) \equiv \mu _j + \varkappa_j \operatorname{Re} \alpha _j > 0forallj,