抄録
We study the convergence or divergence of formal solutions of first order singular nonlinear ordinary differential equation (SE) f(x,u,u′) = 0, u(0)= 0, where the function f is holomorphic in a neighbourhood of the origin of C3. The equation (SE) is said to be singular if f(0,0,ξ) ≡ 0. M. Miyake and A. Shirai [2, 3] already studied this problem in case of partial differential equation and they gave a criterion of convergence or divergence of formal solutions by using the Taylor coefficients of order 1 of formal solution and equation. In this paper, we give a criterion by using the Taylor coefficients of higher order of formal solution and equation.
