Holomorphic and singular solutions of q-difference-differential equations of briot-bouquet type

Hiroshi Yamazawa

doi:10.1619/fesi.59.185

Holomorphic and singular solutions of q-difference-differential equations of briot-bouquet type

Hiroshi Yamazawa

Department of Engineering and Design

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

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 p(x) satisfies p(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).

Original language	English
Pages (from-to)	185-197
Number of pages	13
Journal	Funkcialaj Ekvacioj
Volume	59
Issue number	2
DOIs	https://doi.org/10.1619/fesi.59.185
Publication status	Published - 2016

Keywords

Briot-Bouquet type
Q-analogue
Singular solution

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Geometry and Topology

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10.1619/fesi.59.185

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abstract = "In 1990, G{\'e}rard-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 p(x) satisfies p(0) ∉ {1,2,…}. In this paper the author shows existences of holomorphic and singular solutions of the following type of difference-differential equations tDqu = F(t, x, u, ∂xu).",

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journal = "Funkcialaj Ekvacioj",

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AU - Yamazawa, Hiroshi

PY - 2016

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N2 - 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 p(x) satisfies p(0) ∉ {1,2,…}. In this paper the author shows existences of holomorphic and singular solutions of the following type of difference-differential equations tDqu = F(t, x, u, ∂xu).

AB - 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 p(x) satisfies p(0) ∉ {1,2,…}. In this paper the author shows existences of holomorphic and singular solutions of the following type of difference-differential equations tDqu = F(t, x, u, ∂xu).

KW - Briot-Bouquet type

KW - Q-analogue

KW - Singular solution

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EP - 197

JO - Funkcialaj Ekvacioj

JF - Funkcialaj Ekvacioj

IS - 2

ER -

Holomorphic and singular solutions of q-difference-differential equations of briot-bouquet type

Abstract

Keywords

ASJC Scopus subject areas

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