The paper deals with a singular non-linear partial differential equation t_∂_u/∂_t_ = F(t, x, u, ∂_u_/∂_x_) with two independent variables (t,x) ∈ ℂ2 under the assumption that F(t, x, u, v) is holomorphic and F(0,x,0,0) = 0. Set γ(x) = (∂_F_/∂_v_)(0,x,0,0). In case γ(x) = 0 the equation was investigated quite well by Gerard-Tahara . In case γ(0) = 0 and Re_γ_' < 0 the existence of holomorphic solution was proved in Chen–Tahara  under a non-resonance condition. The present paper proves the existence of holomorphic solution under the same non-resonance condition but using the following weaker condition: γ(0) = 0 and γ'(0) ∈ ℂ\[0, ∞). The result is extended to higher order equations.
Cite this article
Hidetoshi Tahara, Hua Chen, On Totally Characteristic Type Non-linear Partial Differential Equations in the Complex Domain. Publ. Res. Inst. Math. Sci. 35 (1999), no. 4, pp. 621–636