Singular solutions of the Briot-Bouquet type partial differential equations

Coupling of Two Partial Differential Equations and its Application, II — the Case of Briot–Bouquet Type PDEs —

“…About the structure of holomorphic and singular solutions of (1.1) in a neighborhood of (0, 0) ∈ C t × C x , one can refer to Gérard-Tahara [1], [2] and Yamazawa [4]. Among them, the following theorem is the most fundamental result:…”

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

“…For m = 1, Theorem 1 was by Gérard-Tahara [4] and the general case as in Theorem 2 was by Yamazawa [17]. In this paper we will prove Theorem 2 in the general case for m ≥ 1 by a method a little bit different from [17].…”

“…In this paper we will prove Theorem 2 in the general case for m ≥ 1 by a method a little bit different from [17].…”

“…If one of the conditions c-1) ∼ c-3) is not satisfied, the expansion of the solution will be much more complicated as is seen in the case m = 1 by Yamazawa [17], and it seems difficult to describe the expansion in a concrete form. But we can still get the following theorem.…”

Holomorphic and Singular Solutions of <i>q</i>-Difference-Differential Equations of Briot-Bouquet Type

“…Gérard-Tahara [4] and Yamazawa [16] studied the following type of nonlinear singular first order partial di¤erential equations: tq t u ¼ F ðt; x; u; q x uÞ: ð1:8Þ…”