Holomorphic and Singular Solutions of q-Difference-Differential Equations of Briot-Bouquet Type

Abstract

In 1990, Gérard-Tahara [4] introduced the Briot-Bouquet type partial differential equation t∂_tu = F(t,x,u,∂_xu), and they determined the structure of holomorphic and singular solutions provided that the characteristic exponent ρ(x) satisfies ρ(0) ∉ {1,2,...}. In this paper the author shows existences of holomorphic and singular solutions of the following type of difference-differential equations tD_qu = F(t,x,u,∂_xu).