Let us consider the following nonlinear singular partial differential equation

$$
\big(t \frac ∂ {∂_t}\big)^m u = F \Big(t,x,\big\{\big(t\frac ∂ {∂_t} \big)^j\big( \frac ∂  {∂_x}  \big)^α u\big\}_{j+|α|≤ m,j<m}\Big) 
$$

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.

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

Hidetoshi Tahara

Hiroshi Yamazawa

Abstract

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