@unpublished{ChenHidetoshi1998, author = {Chen, Hua and Hidetoshi, Tahara}, title = {On the holomorphic solution of non-linear totally characteristic equations}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25333}, year = {1998}, abstract = {The paper deals with a non-linear singular partial differential equation: (E) t∂/∂t = F(t, x, u, ∂u/∂x) in the holomorphic category. When (E) is of Fuchsian type, the existence of the unique holomorphic solution was established by G{\´e}rard-Tahara [2]. In this paper, 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 The result is extended to higher order case.}, language = {en} } @unpublished{ChenLua1998, author = {Chen, Hua and Lua, Zhuangehu}, title = {On the holomorphic solution of non-linear totally characteristic equations with several space variables}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25189}, year = {1998}, abstract = {In this paper we study a class of non-linear singular partial differential equation in complex domain Csub(t) x C n sub(x). Under certain assumptions, we prove the existence and uniqueness of holomorphic solution near origin of Csub(t) x C n sub(x).}, language = {en} }