On the holomorphic solution of non-linear totally characteristic equations

The paper deals with a non-linear singular partial differential equation (E) t partial derivative/partial derivativet = F(t,x, u, partial derivativeu/partial derivativex) in the holomorphic category. When (E) is of Fuchsian type, the existence of the unique holomorphic solution was established by GERARD - TAHARA [2]. In this pager, under the assumption that (E) is of totally characteristic type, the authors give a sufficient condition for (E) to have a unique holomorphic solution. The result is extended to higher order case.