On Totally Characteristic Type Non-linear Partial Differential Equations in the Complex Domain

  • Hua Chen

    Wuhan University, Wuhan, Hubei, China
  • Hidetoshi Tahara

    Sophia University, Tokyo, Japan

Abstract

The paper deals with a singular non-linear partial differential equation with two independent variables under the assumption that is holomorphic and . Set . In case the equation was investigated quite well by Gérard–Tahara [3]. In case and the existence of holomorphic solution was proved in Chen–Tahara [2] 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: and . The result is extended to higher order equations.

Cite this article

Hua Chen, Hidetoshi Tahara, 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

DOI 10.2977/PRIMS/1195143496