Singular solutions of the Briot-Bouquet type partial differential equations

Abstract

In 1990, Gérard-Tahara [2] introduced the Briot-Bouquet type partial differential equation $t{\partial }_{t}u=F(t,x,u,{\partial }_{x}u)$, and they determined the structure of singular solutions provided that the characteristic exponent $\rho \left(x\right)$ satisfies $\rho \left(0\right)\notin \{1,2,\text{...}\}$. In this paper the author determines the structure of singular solutions in the case $\rho \left(0\right)\in \{1,2,\text{...}\}$.