Singular solutions of the Briot-Bouquet type partial differential equations

摘要

In 1990, Gerard-Tahara introduced the Briot-Bouquet type partial differential equation t partial deriv_tu = F(t, x, u, partial deriv_xu), and they determined the structure of singular solutions provided that the characteristic exponent ρ(x) satisfies ρ(0) is not an element of {1,2,...}. In this paper the author determines the structure of singular solutions in the case ρ(0) ∈ {1,2,...}.