JournalsprimsVol. 41, No. 2pp. 339–373

Structure of Solutions of Nonlinear Partial Differential Equations of Gérard–Tahara Type

  • Hidetoshi Tahara

    Sophia University, Tokyo, Japan
  • Hiroshi Yamazawa

    Caritas Junior College, Yokohama, Japan
Structure of Solutions of Nonlinear Partial Differential Equations of Gérard–Tahara Type cover
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Abstract

Let us consider the following nonlinear singular partial differential equation

(t)m u = F(t,x,{(t)j ()α u}j+|α|≤ m,j<m)
∂_t_∂_t_∂_x_

in the complex domain. When the equation is of Fuchsian type with respect to t, holomorphic and singular solutions were investigated quite well by Gérard–Tahara under some assumptions on characteristic exponents. In this paper, the same type of equations is solved in the general case without any assumption on characteristic exponents.

Cite this article

Hidetoshi Tahara, Hiroshi Yamazawa, Structure of Solutions of Nonlinear Partial Differential Equations of Gérard&#8211;Tahara Type. Publ. Res. Inst. Math. Sci. 41 (2005), no. 2, pp. 339–373

DOI 10.2977/PRIMS/1145475358