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∂_tu=F(t, x, u, ∂_xu), and they determined the structure of singular solutions provided that the characteristic exponent ρ(x) satisfies ρ(0)¬∈{1, 2, ...}. In this paper the author determines the structure of singular solutions in the case ρ(0)∈{1, 2, ...}.